Updated on 2024/12/10

写真a

 
HOSOYA Yuhki
 
Organization
Faculty of Economics Professor
Other responsible organization
Economics Course of Graduate School of Economics, Master's Program
Homepage
http://cf517910.cloudfree.jp/index.html
Profile
I have an interest for all area in the mathematical economics. For microeconomics, I mainly study the general equilibrium thoery, though I also have an interest for game theory. I like Shapley value rather than the Nash equilibrium. For macroeconomics, I have a work in growth theory.
External link

Degree

  • 博士（経済学） ( 慶應義塾大学 )

  • 修士（経済学） ( 慶應義塾大学 )

Education

  • 2010.3
     

    Keio University   doctor course   finished without a degree

  • 2004.3
     

    Keio University   master course   completed

  • 2002.3
     

    Keio University   graduated

  • 1998.3
     

    私立麻布高等学校   graduated

Research History

  • 2023.4 - Now

    Chuo University   Faculty of Economics   Professor

  • 2019.4 - 2023.3

    Chuo University   Faculty of Economics   Associate Professor

  • 2017.4 - 2019.3

    Kanto Gakuin University   College of Economics   Associate Professor

  • 2014.4 - 2017.3

    Kanto Gakuin University   Department of Economics   full-time lecturer

  • 2008.4 - 2011.3

    Keio University   Department of Economics   GS administrator

  • 2008.10 - 2009.9

    Mitsubishi Economic Research Institute   Fulltime Researcher

  • 2004.4 - 2007.3

    Keio University   Department of Economics   Research Assistant

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Professional Memberships

  • JAPANESE ECONOMIC ASSOCIATION

  • The Japanese Society for Mathematical Economics

Research Interests

  • General Equilibrium Theory

  • Dynamic Programming

  • Game Theory

  • Integrability Theory

  • Optimization Theory

  • Theoretical Economics

  • Microeconomics

  • Consumer Theory

  • Frobenius' Theorem

  • Macroeconomics

  • Variational Method

  • Partial Differential Equations

  • Hamilton-Jacobi Equation

Research Areas

  • Humanities & Social Sciences / Economic theory  / Consumer Theory

  • Humanities & Social Sciences / Economic theory  / Optimal Growth Theory

  • Humanities & Social Sciences / Economic theory  / Game Theory

  • Humanities & Social Sciences / Economic theory  / General Equilibrium Theory

  • Natural Science / Applied mathematics and statistics  / Theory of Differential Equations

Papers

  • Non-smooth integrability theory Reviewed International journal

    Yuhki Hosoya

    Economic Theory   78   475 - 520   2024.3

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    Authorship：Lead author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Springer Science and Business Media LLC  

    Abstract

    We study a method for calculating the utility function from a candidate of a demand function that is not differentiable, but is locally Lipschitz. Using this method, we obtain two new necessary and sufficient conditions for a candidate of a demand function to be a demand function. The first concerns the Slutsky matrix, and the second is the existence of a concave solution to a partial differential equation. Moreover, we show that the upper semi-continuous weak order that corresponds to the demand function is unique, and that this weak order is represented by our calculated utility function. We provide applications of these results to econometric theory. First, we show that, under several requirements, if a sequence of demand functions converges to some function with respect to the metric of compact convergence, then the limit is also a demand function. Second, the space of demand functions that have uniform Lipschitz constants on any compact set is compact under the above metric. Third, the mapping from a demand function to the calculated utility function becomes continuous. We also show a similar result on the topology of pointwise convergence.

    DOI： 10.1007/s00199-024-01564-x

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    Other Link： https://link.springer.com/article/10.1007/s00199-024-01564-x/fulltext.html

  • On the fragility of the basis on the Hamilton–Jacobi–Bellman equation in economic dynamics Reviewed International journal

    Yuhki Hosoya

    Journal of Mathematical Economics   111   102940 - 102940   2024.1

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    Authorship：Lead author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)  

    In this paper, we provide an example of the optimal growth model in which there exist infinitely many solutions to the Hamilton–Jacobi–Bellman equation but the value function does not satisfy this equation. We consider the cause of this phenomenon, and find that the lack of a solution to the original problem is crucial. We show that under several conditions, there exists a solution to the original problem if and only if the value function solves the Hamilton–Jacobi–Bellman equation. Moreover, in this case, the value function is the unique nondecreasing concave solution to the Hamilton–Jacobi–Bellman equation. We also show that without our conditions, this uniqueness result does not hold.

    DOI： 10.1016/j.jmateco.2024.102940

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  • The consumption multiplier of government spending: the role of substitutability between government spending and leisure

    Masataka Eguchi, Yuhki Hosoya, Mai Yamada

    Economics Letters   111557 - 111557   2024.1

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    Publishing type：Research paper (scientific journal)   Publisher：Elsevier BV  

    DOI： 10.1016/j.econlet.2024.111557

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  • A Rigorous Proof of the Index Theorem for Economists Reviewed International journal

    Yuhki Hosoya

    Communications in Economics and Mathematical Sciences   2   11 - 30   2023.3

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    Language：English   Publishing type：Research paper (scientific journal)  

    This paper provides a rigorous and gap-free proof of the index theorem used in the theory of regular economy. In the index theorem that is the subject of this paper, the assumptions for the excess demand function are only several usual assumptions and continuous differentiability around any equilibrium price, and thus it has a form that is applicable to many economies. However, the textbooks on this theme contain only abbreviated proofs, and no known monograph contains a rigorous proof of this theorem. Hence, the purpose of this paper is to make this theorem available to more economists by constructing a readable proof.

    DOI： 10.50906/cems.2.0_11

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  • On the basis of the Hamilton–Jacobi–Bellman equation in economic dynamics Reviewed International journal

    Yuhki Hosoya

    Physica D: Nonlinear Phenomena   446   133684 - 133684   2023.2

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：Elsevier BV  

    We consider the classical Ramsey–Cass–Koopmans capital accumulation model and present three examples in which the Hamilton–Jacobi–Bellman (HJB) equation is neither necessary nor sufficient for a function to be the value function. Next, we present assumptions under which the HJB equation becomes a necessary and sufficient condition for a function to be the value function, and using this result, we propose a new method for solving the original problem using the solution to the HJB equation. Our assumptions are so mild that many macroeconomic growth models satisfy them. Therefore, our results ensure that the solution to the HJB equation is rigorously the value function in many macroeconomic models, and present a new solving method for these models.

    DOI： 10.1016/j.physd.2023.133684

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  • An elementary proof of the Euler equation in growth theory Reviewed International journal

    Yuhki Hosoya

    Keio Economic Studies   56   23 - 38   2023

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    Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Keio University  

    In this paper, we derive the Euler equation in a continuous-time macroeconomic dynamic model using only elementary mathematical knowledge. We also provide a proof that the Euler equation and transversality condition are sufficient conditions for the optimal solution. To understand the proofs in this paper, no knowledge of Lebesgue integrals is required. Readers require only some basic mathematical knowledge.

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  • Differential characterization of quasi-concave functions without twice differentiability Invited Reviewed International journal

    Yuhki Hosoya

    Communications in Optimization Theory   2022.11

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    Authorship：Corresponding author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Mathematical Research Press  

    This paper presents a necessary and sufficient condition for a real-valued function defined on an open and convex subset of a Banach space to be quasi-concave, and a sufficient condition for such a function to be strictly quasi-concave. These conditions are applicable to continuously differentiable functions that satisfy a mild additional assumption, and do not require the functions to be twice differentiable. Because this additional assumption is trivially satisfied for twice continuously differentiable functions, our results are pure extensions to classical results.

    DOI： 10.23952/cot.2022.21

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  • Continuous adjustments and Smale’s non-tâtonnement processes International journal

    Chaowen Yu, Yuhki Hosoya

    Journal of Mathematical Economics   100   102619 - 102619   2022.5

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：Elsevier BV  

    In this study, we investigate the stability of the set of equilibria under non-tâtonnement processes formulated by Smale, and show that under a natural assumption named “continuous adjustment”, every nonextendable non-tâtonnement process converges to some point in the set of equilibria. Moreover, we show that such a process can be constructed.

    DOI： 10.1016/j.jmateco.2021.102619

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  • On the approximate purification of mixed strategies in games with infinite action sets Reviewed

    Yuhki Hosoya, Chaowen Yu

    Economic Theory Bulletin   10 ( 1 )   69 - 93   2022.5

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    Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Springer Science and Business Media LLC  

    Abstract

    We consider a game in which the action set of each player is uncountable, and show that, from weak assumptions on the common prior, any mixed strategy has an approximately equivalent pure strategy. The assumption of this result can be further weakened if we consider the purification of a Nash equilibrium. Combined with the existence theorem for a Nash equilibrium, we derive an existence theorem for a pure strategy approximated Nash equilibrium under sufficiently weak assumptions. All of the pure strategies we derive in this paper can take a finite number of possible actions.

    DOI： 10.1007/s40505-022-00219-1

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    Other Link： https://link.springer.com/article/10.1007/s40505-022-00219-1/fulltext.html

  • On the Characterization Theorem for a Solution of Laibson's Hyperbolic Discounting Model Invited

    Yuhki Hosoya

    Keizaikei   285   11 - 25   2022.3

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    Authorship：Lead author   Language：Japanese   Publishing type：Research paper (scientific journal)  

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  • An axiom for concavifiable preferences in view of Alt’s theory Reviewed International journal

    Yuhki Hosoya

    Journal of Mathematical Economics   98   102583 - 102583   2022.1

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    Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Elsevier BV  

    We present a necessary and sufficient condition for Alt’s system to be represented by a continuous utility function. Moreover, we present a necessary and sufficient condition for this utility function to be concave. The latter condition can be seen as an extension of Gossen’s first law, and thus has an economic interpretation. Together with the above results, we provide a necessary and sufficient condition for Alt’s utility to be continuously differentiable.

    DOI： 10.1016/j.jmateco.2021.102583

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  • Consumer Optimization and a First-Order PDE with a Non-Smooth System Reviewed

    Yuhki Hosoya

    Operations Research Forum   2 ( 4 )   2021.12

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    Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Springer Science and Business Media LLC  

    We study a first-order nonlinear partial differential equation and present a necessary and sufficient condition for the global existence of its solution in a non-smooth environment. Using this result, we prove a local existence theorem for a solution to this differential equation. Moreover, we present two applications of this result. The first concerns an inverse problem called the integrability problem in microeconomic theory and the second concerns an extension of Frobenius’ theorem.

    DOI： 10.1007/s43069-021-00104-w

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    Other Link： https://link.springer.com/article/10.1007/s43069-021-00104-w/fulltext.html

  • Formula of the overtaking optimal solution for a growth model with AK technology Invited Reviewed International journal

    Yuhki Hosoya, Susumu Kuwata

    Pure and Applied Functional Analysis   6 ( 5 )   939 - 947   2021.9

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    Authorship：Lead author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Yokohama Publisher  

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  • Equivalence between Nikliborc's theorem and Frobenius' theorem Invited Reviewed International journal

    Yuhki Hosoya

    Pure and Applied Functional Analysis   6 ( 4 )   719 - 741   2021.7

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    Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Yokohama Publisher  

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  • The weak axiom of revealed preference and inverse problems in consumer theory Invited Reviewed International journal

    Yuhki Hosoya

    Linear and Nonlinear Analysis   7 ( 1 )   19 - 31   2021

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  • Recoverability revisited Reviewed International journal

    Yuhki Hosoya

    Journal of Mathematical Economics   90   31 - 41   2020.10

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    Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Elsevier BV  

    This study considers the uniqueness problem of the preference relation corresponding to a demand function, which is called the “recoverability problem”. We show that if a demand function has sufficiently wide range and is income-Lipschitzian, then there exists a unique corresponding upper semi-continuous preference relation. Moreover, we explicitly construct a utility function that represents this preference relation. Compared with related research, a feature of our result is that it ensures not only the uniqueness, but also the existence of the corresponding upper semi-continuous preference relation. Further, we introduce two axioms related to demand functions, and show that these axioms are equivalent to the continuity of our preference relation in the interior of the consumption set. In addition to these results, we present three examples that explain why our requirements (including the upper semi-continuity of preference relations and the wide range requirement and income-Lipschitzian property of demand functions) are necessary, and a further two examples in which there is no continuous preference relation corresponding to the given demand function.

    DOI： 10.1016/j.jmateco.2020.05.009

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  • On the Euler Equation and the Transversality Condition of Overtaking Optimal Solution in Macroeconomic Dynamics

    Yuhki Hosoya

    2019.9

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    Language：English   Publisher：Chuo University  

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  • On an Application of Integration by Change of Variables for Fixed Point Theory

    Yuhki Hosoya

    The Annual Report of Research Institute for Economics and Business Administration Kanto Gakuin University   41   36 - 45   2019.3

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    Language：Japanese   Publishing type：Research paper (scientific journal)  

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  • An Introduction of Ordinary Differential Equations for Economists Reviewed

    Yuhki Hosoya

    Mita Gakkai Zasshi   111 ( 4 )   63 - 89   2019.1

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    Language：Japanese   Publishing type：Research paper (scientific journal)  

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  • The Magic of Capital Reviewed International journal

    Yuhki Hosoya

    Proceedings of The Tenth International Conference on Nonlinear Analysis and Convex Analysis   91 - 108   2019

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    Authorship：Lead author   Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：Yokohama Publisher  

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  • Revealed Preference Theory Reviewed

    Yuhki Hosoya

    Applied Analysis and Optimization   3 ( 2 )   179 - 204   2019

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    Language：English   Publishing type：Research paper (scientific journal)  

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  • First-order partial differential equations and consumer theory Reviewed

    Yuhki Hosoya

    Discrete & Continuous Dynamical Systems - S   11 ( 6 )   1143 - 1167   2018.12

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    Language：English   Publishing type：Research paper (scientific journal)  

    DOI： 10.3934/dcdss.2018065

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  • Nets and Cauchy Sequences Reviewed

    Yuhki Hosoya

    経済系   275   72 - 85   2018.11

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    Language：Japanese   Publishing type：Research paper (scientific journal)  

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  • On the purification of mixed strategies Reviewed

    Chaowen Yu, Yuhki Hosoya, Toru Maruyama

    Economics Bulletin   38 ( 3 )   1655 - 1675   2018.9

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  • Gerald Debreu and Smooth Preferences Reviewed

    Yuhki Hosoya

    Mita Gakkai Zasshi   110 ( 4 )   95 - 131   2018.1

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  • Plausible Equilibria and Backward Payoff-Keeping Behavior Reviewed

    Yuhki Hosoya

    Advances in Mathematical Economics   22   79 - 92   2018

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    Language：English   Publishing type：Research paper (scientific journal)  

    DOI： 10.1007/978-981-13-0605-1_3

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  • The relationship between revealed preference and the Slutsky matrix Reviewed

    Yuhki Hosoya

    JOURNAL OF MATHEMATICAL ECONOMICS   70   127 - 146   2017.5

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：ELSEVIER SCIENCE SA  

    This paper presents a method of calculating the utility function from a smooth demand function whose Slutsky matrix is negative semi-definite and symmetric. The calculated utility function is the unique upper semi-continuous function corresponding with the demand function. Moreover, we present an axiom for demand functions. We show that under the strong axiom, this new axiom is equivalent to the existence of the corresponding continuous preference relation. If the demand function obeys this axiom, the calculated utility function is also continuous. Further, we show that the mapping from the demand function into a continuous preference relation is continuous, which ensures the applicability of our results for econometrics. Moreover, if this demand function satisfies the rank condition, then our utility function is smooth. Finally, we show that under an additional axiom, the above results hold even if the demand function has corner solutions. (C) 2017 The Author(s). Published by Elsevier B.V.

    DOI： 10.1016/j.jmateco.2017.03.001

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  • Excess Information and Tragedy of the Commons Reviewed

    Yuhki Hosoya

    Keio Economic Studies   53   71 - 75   2017

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  • On First-Order Partial Differential Equations: An Existence Theorem and Its Applications Reviewed

    Yuhki Hosoya

    Advances in Mathematical Economics   20   77 - 87   2016.6

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：Springer  

    DOI： 10.1007/978-981-10-0476-6_3

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  • Revealed Preference Theory and the Slutsky Matrix Reviewed

    Yuhki Hosoya

    Mita Gakkai Zasshi   108 ( 3 )   45 - 60   2016.3

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    Language：Japanese   Publishing type：Research paper (scientific journal)  

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  • Directed Position Value

    Yuhki Hosoya

    The Annual Report of Research Institute for Economics and Business Administration Kanto Gakuin University   38   106 - 114   2016.3

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    Language：English   Publishing type：Research paper (scientific journal)  

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  • A Rationalization of Selecting Behavior to Release the Cheap Edition Reviewed

    Yuhki Hosoya

    Economics Bulletin   35 ( 4 )   2617 - 2624   2015.12

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  • Welfare Improvement and the Extension of the Income Gap under Monopoly Reviewed

    Yuhki Hosoya, Soh Kaneko

    Theoretical Economics Letters   5 ( 4 )   590 - 597   2015.8

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    Language：English   Publishing type：Research paper (scientific journal)  

    DOI： 10.4236/tel.2015.54069

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  • The Relationship between Two Definitions of Manifolds Reviewed

    Yuhki Hosoya

    Keizaikei   263   14 - 17   2015.4

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    Language：English   Publishing type：Research paper (scientific journal)  

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  • A Theory for Estimating Consumer’s Preference from Demand Reviewed

    Yuhki Hosoya

    Advances in Mathematical Economics   19   33 - 55   2015

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：Springer  

    DOI： 10.1007/978-4-431-55489-9_2

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  • A Characterization of Quasi-concave Function in View of the Integrability Theory Reviewed

    Yuhki Hosoya

    Advances in Mathematical Economics   18   135 - 140   2014.7

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：Springer  

    DOI： 10.1007/978-4-431-54834-8_4

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  • Identification and testable implications of the Ramsey-Cass-Koopmans model Reviewed

    Yuhki Hosoya

    JOURNAL OF MATHEMATICAL ECONOMICS   50   63 - 68   2014.1

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：ELSEVIER SCIENCE SA  

    This paper aims to provide a method for calculating the utility function and discount rate of the discrete-time Ramsey-Cass-Koopmans model from the policy and production functions. In contrast to similar works, our method ensures the uniqueness of the utility function up to positive affine transformations. Further, we provide a similar result in a stochastic model. (C) 2013 Elsevier B.V. All rights reserved.

    DOI： 10.1016/j.jmateco.2013.12.001

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  • A Formula for Calculating the Slutsky Matrix Reviewed

    Yuhki Hosoya

    Keio Economic Studies   50 ( 1 )   77 - 82   2014

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：Keio Economic Society, Keio University  

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  • On the Continuous-Time Ramsey=Cass=Koopmans Model with CRRA Utility Function Reviewed

    Yuhki Hosoya

    Mita Gakkai Zasshi   106 ( 2 )   41 - 68   2013.7

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  • Measuring utility from demand Reviewed

    Yuhki Hosoya

    JOURNAL OF MATHEMATICAL ECONOMICS   49 ( 1 )   82 - 96   2013.1

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：ELSEVIER SCIENCE SA  

    This study presents a new method to calculate a preference relation from a demand function. Our method works well under the weak axiom and can calculate a smooth utility function if the demand function obeys the strong axiom. Further, if the demand function is derived from a customary utility function, our method restores the original preference. Our method provides a complete and rigorous proof of Samuelson's conjecture. In addition to these results, we guarantee the recoverability: i.e., the uniqueness of the preference relation corresponding to a demand function. (C) 2012 Elsevier B.V. All rights reserved.

    DOI： 10.1016/j.jmateco.2012.10.001

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  • Viable Solutions of Differential Equations and the Stability of Tâtonnement Processes Reviewed

    Yuhki Hosoya, Chaowen Yu

    Mita Gakkai Zasshi   106 ( 1 )   109 - 133   2013

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  • A Fixed Point Theorem and an Application to Bellman Operators Reviewed

    Yuhki Hosoya, Masayuki Yao

    Theoretical Economics Letters   3 ( 01 )   65 - 68   2013

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    Language：English   Publishing type：Research paper (scientific journal)  

    DOI： 10.4236/tel.2013.31010

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  • Partial Differential Equations and the Integrability of Demand Functions : Nikliborc Theorem and Its Applications Reviewed

    Yuhki Hosoya, Chaowen Yu

    Mita Gakkai Zasshi   105 ( 3 )   179 - 197   2012.10

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  • Partial Differential Equations and the Integrability of Inverse Demand Functions : Focusing on Frobenius Theorem Reviewed

    Yuhki Hosoya, Chaowen Yu

    Mita Gakkai Zasshi   105 ( 2 )   139 - 162   2012.7

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  • Elementary Form and Proof of the Frobenius Theorem for Economists Reviewed

    Yuhki Hosoya

    Advances in Mathematical Economics   16   39 - 51   2012

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：Springer  

    DOI： 10.1007/978-4-431-54114-1_2

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  • On Methods for Observing Consumer's Preference

    Yuhki Hosoya

    Keio University   2011.12

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    Language：Japanese   Publishing type：Doctoral thesis  

    File： DT.pdf

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  • An Existence Result and a Characterization of the Least Concave Utility of Homothetic Preferences Reviewed

    Yuhki Hosoya

    Advances in Mathematical Economics   15   123 - 127   2011.4

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    Language：English   Publishing type：Research paper (scientific journal)  

    DOI： 10.1007/978-4-431-53930-8_6

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  • An existence result and a characterization of the least concave utility of quasi-linear preferences Reviewed

    Yuhki Hosoya

    Journal of Mathematical Economics   47 ( 2 )   251 - 252   2011.3

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    Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Elsevier BV  

    DOI： 10.1016/j.jmateco.2011.03.001

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  • Consumer Theory and Plane Geometry Reviewed

    Yuhki Hosoya

    Mita Gakkai Zasshi   102 ( 1 )   161 - 172   2009.4

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  • On Measuring Utility from Demand: without Proof

    Yuhki Hosoya

    RIMS Kokyuroku   1654   56 - 77   2009

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：Kyoto University  

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    Other Link： http://hdl.handle.net/2433/140844

  • An Interpretation of the “Greatest Hits”-like Behavior

    Yuhki Hosoya

    RIMS Kokyuroku   1557   152 - 161   2007

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：Kyoto University  

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    Other Link： http://hdl.handle.net/2433/81017

  • Fiscally Stable Income Distributions under Majority Voting, Lorenz Curves and Bargaining Sets Invited

    Jean-Michel Grandmont, Yuhki Hosoya

    Mita Journal of Economics   98 ( 4 )   39 - 53   2006.1

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  • A Question on the Usefulness of Copyright Protection

    Yuhki Hosoya

    RIMS Kokyuroku   1443   164 - 170   2005

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：Kyoto University  

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    Other Link： http://hdl.handle.net/2433/47589

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Books

  • Theory of Extremal Problems

    A. D. Ioffe, V. M. Tikhomirov, Yuhki Hosoya, Chaowen Yu（ Role： Joint translator）

    Chisen Shokan  2017.3  （ ISBN:9784862852519 ）

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    Total pages：632   Language：Japanese   Book type：Scholarly book

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  • The Origin and Extensions of Mathematical Economics

    Yuhki Hosoya（ Role： Contributorchapter 2）

    2015.9 

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  • A Theory for Calculating Utility Functions

    Yuhki Hosoya（ Role： Sole author）

    Mitsubishi Economic Research Institute  2010.7 

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Presentations

  • The Hamilton-Jacobi-Bellman Equation in Economic Dynamics with a Non-Smooth Fiscal Policy

    Yuhki Hosoya

    Mathematical Economics 2024 workshop  2024.11 

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    Event date： 2024.11 　 　

    Language：Japanese   Presentation type：Oral presentation (general)  

    File： HJeqb4.pdf

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  • Relationship between Consumer Theories with and without Utility Maximization

    Yuhki Hosoya

    The 30th Decentralized Conference  2024.10 

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    Event date： 2024.10 　 　

    Language：Japanese   Presentation type：Oral presentation (general)  

    File： subjectiveb2.pdf

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  • Relationship between Consumer Theories with and without Utility Maximization

    Yuhki Hosoya

    JEA Autumn Meeting 2024  2024.10 

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    Event date： 2024.10 　 　

    Language：Japanese   Presentation type：Oral presentation (general)  

    File： subjectiveb.pdf

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  • Non-Smooth Integrability Theory

    Yuhki Hosoya

    2023 Mathematical Economics workshop  2023.11 

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    Event date： 2023.11 　 　

    Language：Japanese   Presentation type：Oral presentation (general)  

    File： nonsmoothb13.pdf

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  • Utilitarian Theorems and Equivalence of Utility Theories

    Yuhki Hosoya

    2023 Autumn Meeting of Japanese Economic Association  2023.9 

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    Event date： 2023.9 　 　

    Language：Japanese   Presentation type：Oral presentation (general)  

    File： HAb2.pdf

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  • Utilitarian Theorems and Equivalence of Utility Theories

    Yuhki Hosoya

    The 29th DC conference  2023.9 

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    Event date： 2023.9 　 　

    Language：Japanese   Presentation type：Oral presentation (general)  

    File： HAb.pdf

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  • Non-Smooth Integrability Theory Invited

    Yuhki Hosoya

    ICIAM2023  2023.8 

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    Event date： 2023.8 　 　

    Language：English   Presentation type：Oral presentation (general)  

    File： nonsmoothb1e.pdf

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  • Non-Smooth Frobenius' Theorem Invited

    Yuhki Hosoya

    The 13th AIMS conference on Dynamical Systems, Differential Equations and Applications  2023.6 

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    Event date： 2023.5 - 2023.6

    Language：English   Presentation type：Oral presentation (general)  

    File： frobeniusb.pdf

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  • On the Uniqueness and Stability of the Equilibrium Price in Quasi-Linear Economies

    Yuhki Hosoya

    Mathematical Economics 2022 workshop  2022.11 

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    Event date： 2022.11 　 　

    Language：Japanese   Presentation type：Oral presentation (general)  

    File： stabilityb4.pdf

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  • Non-Smooth Integrability Theory

    Yuhki Hosoya

    2022.10 

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    Event date： 2022.10 　 　

    Language：Japanese   Presentation type：Oral presentation (general)  

    File： nonsmoothb10.pdf

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  • On the Uniqueness and Stability of the Equilibrium Price in Quasi-Linear Economies

    Yuhki Hosoya

    2022.10 

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    Event date： 2022.10 　 　

    Language：Japanese   Presentation type：Oral presentation (general)  

    File： stabilityb4.pdf

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  • Violation of the Hamilton-Jacobi-Bellman Equation in Economic Dynamics

    Yuhki Hosoya

    ORCOS:VC2022  2022.7 

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    Event date： 2022.7 　 　

    Language：English   Presentation type：Oral presentation (general)  

    File： HJeqb3.pdf

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  • On the Basis of the Hamilton-Jacobi-Bellman Equation in Economic Dynamics Invited

    2022.5 

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    Language：Japanese   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

    File： HJeqb2.pdf

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  • The Axiom for Concavifiable Preference in View of Alt's Theory

    Yuhki Hosoya

    2021.11 

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    Event date： 2021.11 　 　

    Language：Japanese   Presentation type：Oral presentation (general)  

    File： Altb2.pdf

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  • On the Uniqueness and Stability of the Equilibrium Price in Quasi-Linear Economies

    Yuhki Hosoya

    2021.10 

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    Event date： 2021.10 　 　

    Language：Japanese   Presentation type：Oral presentation (general)  

    File： stabilityb3.pdf

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  • Violation of the Hamilton-Jacobi-Bellman Equation in Economic Dynamics Invited

    Yuhki Hosoya

    Kanto-Gakuin University Keizai Keiei Kenkyusho seminar  2021.3 

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    Language：Japanese   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

    File： HJeqb.pdf

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  • The Violation of the Hamilton-Jacobi-Bellman Equation in Economic Dynamics

    Yuhki Hosoya

    Mathematical Economics 2020 Workshop  2020.11 

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    Event date： 2020.11 　 　

    Language：Japanese   Presentation type：Oral presentation (general)  

    File： HJeqb.pdf

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  • On the Uniqueness and Stability of the Equilibrium Price in Quasi-Linear Economies

    Yuhki Hosoya

    2020.11 

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    Language：English   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

    File： stabilityb2.pdf

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  • The Axiom for Concavifiable Preference in view of Alt's Theory

    Yuhki Hosoya

    2020 Autumn Meeting of the Japanese Economic Association  2020.10 

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    Event date： 2020.10 　 　

    Language：Japanese   Presentation type：Oral presentation (general)  

    File： Altb.pdf

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  • Shephard's Lemma and Non-Smooth Integrability Theory

    Yuhki Hosoya

    2019.11 

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    Language：Japanese   Presentation type：Oral presentation (general)  

    File： nonsmoothb8.pdf

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  • Shephard's Lemma and Non-Smooth Integrability Theory

    Yuhki Hosoya

    2019.10 

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    Language：Japanese   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

    File： nonsmoothb7.pdf

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  • Shephard's Lemma and Non-Smooth Integrability Theory

    Yuhki Hosoya

    2019.10 

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    Language：Japanese   Presentation type：Oral presentation (general)  

    File： nonsmoothb5.pdf

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  • 消費者理論に残された課題

    細矢祐誉

    関東学院大学経済経営研究所プロジェクト講演会  2019.9 

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    Language：Japanese   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

    File： consumerb.pdf

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  • Shephard's Lemma and Non-Smooth Integrability Theory International conference

    Yuhki Hosoya

    NACA-ICOTA2019  2019.8 

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    Language：English   Presentation type：Oral presentation (general)  

    File： nonsmootheb3.pdf

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  • Non-Smooth Integrability Theory Invited International conference

    Yuhki Hosoya

    ICIAM2019  2019.7 

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    Language：English   Presentation type：Oral presentation (invited, special)  

    File： nonsmootheb3.pdf

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  • On Alt's Utility Theory

    Yuhki Hosoya

    2019.7 

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    Language：Japanese   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

    File： altb2.pdf

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  • Shephard's Lemma as a Partial Differential Equation Invited

    Yuhki Hosoya

    2018.11 

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    Language：English   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

    File： nonsmootheb2.pdf

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  • Shephard's Lemma and Partial Differential Equations Invited International conference

    Yuhki Hosoya

    6th Conference of Nonlinear Analysis and Optimization  2018.11 

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    Language：English   Presentation type：Oral presentation (invited, special)  

    File： nonsmootheb.pdf

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  • On the Hamilton-Jacobi-Bellman Equation of Macroeconomic Dynamics Invited

    Yuhki Hosoya

    2018.10 

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    Language：Japanese   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

    File： kuwatab9.pdf

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  • Non-Smooth Integrability Theory and Partial Differential Equations

    Yuhki Hosoya

    Mathematical Economics 2018 Workshop at Kyoto  2018.10 

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    Language：Japanese   Presentation type：Oral presentation (general)  

    File： nonsmoothb4.pdf

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  • On the Hamilton-Jacobi-Bellman Equation of Macroeconomic Dynamics

    Yuhki Hosoya

    2018.9 

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    Language：Japanese   Presentation type：Oral presentation (general)  

    File： kuwatab8.pdf

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  • Shephard's Lemma as a Partial Differential Equation

    Yuhki Hosoya

    The 24th Decentralization Conference  2018.9 

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    Language：Japanese   Presentation type：Oral presentation (general)  

    File： nonsmoothb3.pdf

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  • On the Hamilton-Jacobi-Bellman Equation of Macroeconomic Dynamics Invited International conference

    Yuhki Hosoya

    The 12th AIMS Conference on Dynamical Systems, Differential Equations and Applications  2018.7 

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    Language：English   Presentation type：Oral presentation (invited, special)  

    File： kuwataeb4.pdf

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  • Non-Smooth Integrability Theory

    Yuhki Hosoya

    Mathematical Economics October 2017 Workshop at Keio  2017.10 

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    Language：Japanese   Presentation type：Oral presentation (general)  

    File： nonsmoothb2.pdf

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  • The Euler Equation and the Transversality Condition of Macroeconomic Dynamics Invited International conference

    Yuhki Hosoya

    SIAM Conference on Control and Its Application  2017.7 

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    Language：English   Presentation type：Oral presentation (invited, special)  

    File： kuwataeb3.pdf

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  • The Hamilton-Jacobi-Bellman Equation of Macroeconomic Dynamics Invited International conference

    Yuhki Hosoya

    The 10th Anniversary Conference on Nonlinear Analysis and Convex Analysis  2017.7 

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    Language：English   Presentation type：Oral presentation (invited, special)  

    File： kuwataeb2.pdf

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  • On the Euler Equation of Macroeconomic Dynamics

    Yuhki Hosoya

    2017.6 

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    Language：Japanese   Presentation type：Oral presentation (general)  

    File： kuwatab5.pdf

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  • Overtaking Criterion for Unbounded Optimal Growth Models with a Linear Technology International conference

    Yuhki Hosoya

    Mathematical Economics 2017 Workshop at Keio  2017.3 

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    Language：English   Presentation type：Oral presentation (general)  

    File： kuwataeb.pdf

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  • Non-Smooth Integrability Theory

    Yuhki Hosoya

    Workshop on Microeconomics in Institute of Economic Studies at Keio University  2016.11 

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    Language：Japanese   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

    File： nonsmoothb.pdf

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  • The Recoverability Revisited

    Yuhki Hosoya

    The 22nd Decentralization Conference in Japan  2016.8 

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    Language：Japanese   Presentation type：Oral presentation (general)  

    File： howtob13.pdf

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  • The Relationship between Revealed Preference and Slustky Matrix Invited International conference

    Yuhki Hosoya

    The 11th AIMS Conference on Dynamical Systems, Differential Equations and Applications  2016.7 

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    Language：English   Presentation type：Oral presentation (invited, special)  

    File： howtob12e.pdf

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  • On the Slutsky Matrix of the Demand Function and A Calculation Method for Utility

    Yuhki Hosoya

    2016.6 

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    Language：Japanese   Presentation type：Oral presentation (general)  

    File： howtob11.pdf

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  • Relationship between Revealed Preference and Slutsky Matrix International conference

    Yuhki Hosoya

    2016 :: Joint Mathematical Meetings  2016.1 

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    Language：English   Presentation type：Oral presentation (general)  

    File： Hosoya2016-1.pdf

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  • The Relationship between Revealed Preference and the Slutsky Matrix International conference

    Yuhki Hosoya

    RIMS Workshop "Mathematical Analysis in Economic Theory"  2015.11 

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    Language：English   Presentation type：Oral presentation (general)  

    File： howtob6e.pdf

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  • The Relationship between Revealed Preference and the Slutsky Matrix

    Yuhki Hosoya

    The 21st Decentralization Conference in Japan  2015.10 

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    Language：Japanese   Presentation type：Oral presentation (general)  

    File： howtob6.pdf

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  • The Problem on the Transmission of the Consistency - the Reverse-Calculation Problem of Consumer's Preference from Demand

    Yuhki Hosoya

    The 7th Conference of Macroeconomic Policy and Analysis  2015.8 

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    Language：Japanese   Presentation type：Oral presentation (general)  

    File： howtob5.pdf

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  • A Reverse Calculation Method to the Utility Function from the Policy Function for Dynamic Optimal Growth Models Invited International conference

    Yuhki Hosoya

    13th Viennese Workshop on Optimal Control and Dynamic Games  2015.5 

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    Language：English   Presentation type：Oral presentation (invited, special)  

    File： rckb3.pdf

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  • The Relationship between Revealed Preference Theory and the Slutsky Matrix International conference

    Yuhki Hosoya

    The 6 th Conference on Mathematical Analysis in Economic Theory  2015.1 

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    Language：English   Presentation type：Oral presentation (general)  

    File： howtob4.pdf

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  • A Theory for Estimating Consumer’s Preference from Demand Invited International conference

    Yuhki Hosoya

    IFORS2014  2014.7 

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    Language：English   Presentation type：Oral presentation (invited, special)  

    File： howtob3.pdf

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  • A Theory to Estimate Consumer’s Preference from Demand

    Yuhki Hosoya

    2013.12 

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    Language：Japanese   Presentation type：Oral presentation (general)  

    File： Howtob.pdf

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  • A Reverse Calculation from Policy Function to Utility Function in Optimal Growth Model

    Yuhki Hosoya

    2013.8 

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    Language：Japanese   Presentation type：Oral presentation (general)  

    File： rcksb.pdf

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  • The Reverse Calculation Method for Utility Function of Ramsey-Cass-Koopmans Model

    Yuhki Hosoya

    2012.11 

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    Language：Japanese   Presentation type：Oral presentation (general)  

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  • On the Substitute-Complementary Relationships of Commodities

    Yuhki Hosoya

    2010.11 

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    Language：English   Presentation type：Oral presentation (general)  

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  • On Measuring Utility from Demand

    Yuhki Hosoya

    2008.11 

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    Language：Japanese   Presentation type：Oral presentation (general)  

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  • An Interpretation of the “Greatest Hits”-like Behavior

    Yuhki Hosoya

    2006.12 

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    Language：Japanese   Presentation type：Oral presentation (general)  

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  • Excess Information and Tragedy of the Commons

    Yuhki Hosoya

    2005.11 

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    Language：Japanese   Presentation type：Oral presentation (general)  

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  • A Question for the Usefulness of Copyright Protection

    Yuhki Hosoya

    2005.2 

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    Language：Japanese   Presentation type：Oral presentation (general)  

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Research Projects

  • On Applications for partial differential equations in non-smooth systems to consumer theory and econometric theory

    Grant number：21K01403  2021.4 - 2024.3

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)  Grant-in-Aid for Scientific Research (C)  Chuo University

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    Authorship：Principal investigator 

    Grant amount： \4160000 （ Direct Cost: \3200000 、 Indirect Cost： \960000 ）

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  • 積分可能性理論のnon-smooth的展開とその計量経済学的応用について

    2018.4 - 2021.3

    日本学術振興会  科学研究費助成制度・若手研究 

    細矢祐誉

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    Authorship：Principal investigator  Grant type：Competitive

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  • A Characterization of Solutions for Cooperative Fuzzy Games: Solutions via Markets and Mechanism Design

    Grant number：26380246  2014.4 - 2018.3

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)  Hosei University

    SAGARA Nobusumi, MIYAZAKI Kenji, HOSOYA Yuhki, Khan Mohammed Ali, Mordukhovich Boris S., SUZUKI Takashi

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    Grant amount： \4810000 （ Direct Cost: \3700000 、 Indirect Cost： \1110000 ）

    The purpose of this research was to investigate cooperative behaviors of players with fuzzy coalitions, establish the method for deriving the solutions via market mechansim, and clarify its limitation to provide an insights into practical problems on group decision-making. Toward this end, we formulated the fuzzy extension to fuzzify cooperative games and characterized the class of fuzzy games and their fuzy extension such that the fuzzy core coincides with the original cooperative games. For the cooperative games that lack the core, we proposed the alternative concept, called a fuzzy Weber set, and charcaterized the fuzzy extensions such that the fuzzy Weber set coincides with the Weber set of the original cooperative game.

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Allotted class

  • 2024   Introductory Macroeconomics   Department

  • 2024   Introductory Microeconomics   Department

  • 2024   Seminar 1   Department

  • 2024   Seminar 2   Department

  • 2024   Seminar Thesis   Department

  • 2024   Interdisciplinary Lecture III   Department

  • 2024   MicroeconomicsⅠ   Graduate school

  • 2024   MicroeconomicsⅡ   Graduate school

  • 2024   Seminar Ⅰ(Microeconomics)   Graduate school

  • 2024   Seminar Ⅱ(Microeconomics)   Graduate school

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Teaching Experience

  • Seminar (Microeconomics)

    2023.4 - Now   Institution：Chuo University

  • 総合講座III

    2021.9 - Now   Institution：中央大学

  • Seminar

    2020.4 - Now   Institution：Chuo University

  • Seminar for Mathematical Economics

    2020.4 - Now   Institution：Keio University

  • Microeconomics

    2019.4 - Now   Institution：Chuo University

  • Elementary Macroeconomics

    2019.4 - Now   Institution：Chuo University

  • Elementary Microeconomics

    2019.4 - Now   Institution：Chuo University

  • Mathematics for Economics

    2023.9 - 2024.3   Institution：Hosei University

  • Mathematics

    2023.9 - 2024.3   Institution：Hosei University

  • applied microeconomics

    2020.4 - 2022.3   Institution：Komazawa University

  • Microeconomics

    2018.4 - 2019.3   Institution：Hosei University

  • Mathematical Economics

    2017.4 - 2019.3   Institution：Kanto Gakuin University

  • preseminar

    2014.4 - 2019.3   Institution：Kanto Gakuin University

  • Elementary Seminar

    2014.4 - 2019.3   Institution：Kanto Gakuin University

  • Mathematics for Economics

    2014.4 - 2019.3   Institution：Kanto Gakuin University

  • Mathematics for Economics

    2017.4 - 2018.3   Institution：Hosei University

  • Seminar

    2014.4 - 2018.3   Institution：Kanto Gakuin University

  • KGUキャリアデザイン入門

    2015.4 - 2017.3   Institution：Kanto Gakuin University

  • Mathematics for Economics

    2016.4 - 2016.6   Institution：The University of Tokyo

  • Special Lecture on Mathematics for Economics

    2014.4 - 2015.3   Institution：Kanto Gakuin University

  • Macroeconomics

    2012.4 - 2014.3   Institution：Nihon University

  • Elementary Mathematics for Economics

    2010.4 - 2014.3   Institution：Kanagawa University

  • Principle of Economics

    2010.9 - 2013.12   Institution：Keio University

  • Micoreconomics

    2012.4 - 2013.3   Institution：Nihon University

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Committee Memberships

  • 2020.4 - 2024.3

    Japanese Society of Mathematical Economics   評議員  

  • 2019.4 - 2023.3

    Japanese Society of Mathematical Economics   研究集会担当理事