記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：Springer  

DOI： 10.1007/s10107-017-1181-0

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：SPRINGER  

This paper studies unified formulations of support vector machines (SVMs) for binary classification on the basis of convex analysis, especially, convex risk functions theory, which is recently developed in the context of financial optimization. Using the notions of convex empirical risk and convex regularizer, a pair of primal and dual formulations of the SVMs are described in a general manner. With the generalized formulations, we discuss reasonable choices for the empirical risk and the regularizer on the basis of the risk function's properties, which are well-known in the financial context. In particular, we use the properties of the risk function's dual representations to derive multiple interpretations. We provide two perspectives on robust optimization modeling, enhancing the known facts: (1) the primal formulation can be viewed as a robust empirical risk minimization; (2) the dual formulation is compatible with the distributionally robust modeling.

DOI： 10.1007/s10479-016-2326-x

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記述言語：日本語   掲載種別：研究論文（学術雑誌）   出版者・発行元：朝倉書店  

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：Springer  

DOI： 10.1007/s10107-015-0899-9

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：Springer  

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記述言語：日本語   掲載種別：研究論文（学術雑誌）   出版者・発行元：日本オペレーションズ・リサーチ学会  

CiNii Books

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：ELSEVIER  

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記述言語：日本語   掲載種別：研究論文（学術雑誌）  

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：TAYLOR & FRANCIS LTD  

In this article we propose a simple heuristic algorithm for approaching the maximally predictable portfolio, which is constructed so that return model of the resulting portfolio would attain the largest goodness-of-fit. It is obtained by solving a fractional program in which a ratio of two convex quadratic functions is maximized, and the number of variables associated with its nonconcavity has been a bottleneck in spite of continuing endeavour for its global optimization. The proposed algorithm can be implemented by simply solving a series of convex quadratic programs, and computational results show that it yields within a few seconds a (near) Karush-Kuhn-Tucker solution to each of the instances which were solved via a global optimization method in [H. Konno, Y. Takaya and R. Yamamoto, A maximal predictability portfolio using dynamic factor selection strategy, Int. J. Theor. Appl. Fin. 13 (2010) pp. 355-366]. In order to confirm the solution accuracy, we also pose a semidefinite programming relaxation approach, which succeeds in ensuring a near global optimality of the proposed approach. Our findings through computational experiments encourage us not to employ the global optimization approach, but to employ the local search algorithm for solving the fractional program of much larger size.

DOI： 10.1080/02331934.2012.741237

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：Taylor & Francis  

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：Springer  

Index tracking is a passive investment strategy in which a fund (e. g., an ETF: exchange traded fund) manager purchases a set of assets to mimic a market index. The tracking error, i. e., the difference between the performances of the index and the portfolio, may be minimized by buying all the assets contained in the index. However, this strategy results in a considerable transaction cost and, accordingly, decreases the return of the constructed portfolio. On the other hand, a portfolio with a small cardinality may result in poor out-of-sample performance. Of interest is, thus, constructing a portfolio with good out-of-sample performance, while keeping the number of assets invested in small (i. e., sparse). In this paper, we develop a tracking portfolio model that addresses the above conflicting requirements by using a combination of L0- and L2-norms. The L2-norm regularizes the overdetermined system to impose smoothness (and hence has better out-of-sample performance), and it shrinks the solution to an equally-weighted dense portfolio. On the other hand, the L0-norm imposes a cardinality constraint that achieves sparsity (and hence a lower transaction cost). We propose a heuristic method for estimating portfolio weights, which combines a greedy search with an analytical formula embedded in it. We demonstrate that the resulting sparse portfolio has good tracking and generalization performance on historic data of weekly and monthly returns on the Nikkei 225 index and its constituent companies. © 2012 Springer-Verlag Berlin Heidelberg.

DOI： 10.1007/s10287-012-0158-y

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記述言語：日本語   出版者・発行元：MTEC  

CiNii Books

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：ELSEVIER SCIENCE BV  

In this paper, we derive a portfolio optimization model by minimizing upper and lower bounds of loss probability. These bounds are obtained under a nonparametric assumption of underlying return distribution by modifying the so-called generalization error bounds for the support vector machine, which has been developed in the field of statistical learning. Based on the bounds, two fractional programs are derived for constructing portfolios, where the numerator of the ratio in the objective includes the value-at-risk (VaR) or conditional value-at-risk (CVaR) while the denominator is any norm of portfolio vector. Depending on the parameter values in the model, the derived formulations can result in a nonconvex constrained optimization, and an algorithm for dealing with such a case is proposed. Some computational experiments are conducted on real stock market data, demonstrating that the CVaR-based fractional programming model outperforms the empirical probability minimization. (C) 2011 Elsevier B.V. All rights reserved.

DOI： 10.1016/j.ejor.2011.09.012

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：Springer  

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記述言語：日本語   掲載種別：研究論文（学術雑誌）   出版者・発行元：日本オペレーションズ・リサーチ学会  

本論文では,東証業種別株価指数の推移データに因子分析を施した結果を用いて企業価値変動モデルを構築し,それに基づいてデフォルトのシナリオを発生させ,リスク尺度としてConditional Value-at-Riskを用いて与信の最適化を行った.これにより経済動向を示す共通因子の影響を,「共通因子の個数」と「共通因子と個別因子の影響の比を決めるパラメータ」の両者を変化させて観察した.解くべき最適化問題の規模はシナリオの個数に影響を受けるため,多数のシナリオを用いて問題を解くことは易しくないが,問題の構造を利用して,簡単な前処理と解法の工夫によって10万シナリオの問題を7秒程度で,50万シナリオの問題を35秒程度で解くことに成功した.

DOI： 10.15807/torsj.54.23

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：Springer  

Several optimization approaches for portfolio selection have been proposed in order to alleviate the estimation error in the optimal portfolio. Among them are the norm-constrained variance minimization and the robust portfolio models. In this paper, we examine the role of the norm constraint in portfolio optimization from several directions. First, it is shown that the norm constraint can be regarded as a robust constraint associated with the return vector. Second, the reformulations of the robust counterparts of the value-at-risk (VaR) and conditional value-at-risk (CVaR) minimizations contain norm terms and are shown to be highly related to the ν-support vector machine (ν-SVM), a powerful statistical learning method. For the norm-constrained VaR and CVaR minimizations, a nonparametric theoretical validation is posed on the basis of the generalization error bound for the ν-SVM. Third, the norm-constrained approaches are applied to the tracking portfolio problem. Computational experiments reveal that the norm-constrained minimization with a parameter tuning strategy improves on the traditional norm-unconstrained models in terms of the out-of-sample tracking error. © 2011 Springer-Verlag.

DOI： 10.1007/s10287-011-0130-2

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：Springer  

We study the constant rebalancing strategy for multi-period portfolio optimization via conditional value-at-risk (CVaR) when there are nonlinear transaction costs. This problem is difficult to solve because of its nonconvexity. The nonlinear transaction costs and CVaR constraints make things worse
state-of-the-art nonlinear programming (NLP) solvers have trouble in reaching even locally optimal solutions. As a practical solution, we develop a local search algorithm in which linear approximation problems and nonlinear equations are iteratively solved. Computational results are presented, showing that the algorithm attains a good solution in a practical time. It is better than the revised version of an existing global optimization. We also assess the performance of the constant rebalancing strategy in comparison with the buy-and-hold strategy. © 2010 Springer Science+Business Media, LLC.

DOI： 10.1007/s10690-010-9130-4

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：SPRINGER  

In financial engineering, one often encounters barrier options in which an action promised in the contract is taken if the underlying asset value becomes too high or too low. In order to compute the corresponding prices, it is necessary to capture the dynamic behavior of the associated stochastic process modified by boundaries. To the best knowledge of the authors, there is no algorithmic approach available to compute such prices repeatedly in a systematic manner. The purpose of this paper is to develop computational algorithms to capture the dynamic behavior of Ornstein-Uhlenbeck processes modified by various boundaries based on the Ehrenfest approximation approach established in Sumita et al. (J Oper Res Soc Jpn 49:256-278, 2006). As an application, we evaluate the prices of up-and-out call options maturing at time tau(M) with strike price K(S) written on a discount bond maturing at time T, demonstrating the usefulness, speed and accuracy of the proposed computational algorithms.

DOI： 10.1007/s11009-009-9152-4

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記述言語：英語   掲載種別：研究論文（国際会議プロシーディングス）   出版者・発行元：Operations Research Society of Japan  

We build a computational framework for determining an optimal dynamic asset allocation over multiple periods. To do this, we use a nonlinear control policy, which is a function of past returns of investable assets. By employing a kernel method, the problem of selecting the best control policy from among nonlinear functions can be formulated as a convex quadratic optimization problem. Furthermore, we reduce the problem to a linear optimization problem by employing Li-norm regularization. A numerical experiment was conducted wherein scenarios of the rate of return of investable assets were generated by using a one-period autoregressive model, and the results showed that our investment strategy improves an investment performance more than other strategies from previous studies do. © The Operations Research Society of Japan.

DOI： 10.15807/jorsj.54.201

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：SPRINGER  

In this paper, we address an approximate solution of a probabilistically constrained convex program (PCCP), where a convex objective function is minimized over solutions satisfying, with a given probability, convex constraints that are parameterized by random variables. In order to approach to a solution, we set forth a conservative approximation problem by introducing a parameter alpha which indicates an approximate accuracy, and formulate it as a D.C. optimization problem.
As an example of the PCCP, the Value-at-Risk (VaR) minimization is considered under the assumption that the support of the probability of the associated random loss is given by a finitely large number of scenarios. It is advantageous in solving the D.C. optimization that the numbers of variables and constraints are independent of the number of scenarios, and a simplicial branch-and-bound algorithm is posed to find a solution of the D.C. optimization. Numerical experiments demonstrate the following: (i) by adjusting a parameter alpha, the proposed problem can achieve a smaller VaR than the other convex approximation approaches; (ii) when the number of scenarios is large, a typical 0-1 mixed integer formulation for the VaR minimization cannot be solved in a reasonable time and the improvement of the incumbent values is slow, whereas the proposed method can achieve a good solution at an early stage of the algorithm.

DOI： 10.1007/s10589-008-9178-5

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記述言語：英語  

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：Institutional Investor, Inc  

The Hull-White model is a one factor Markov model well known for its capability to capture the current term structure of interest rates. Analytical results are available for pricing zero-coupon discount bonds and associated European options when both reversion and volatility functions are constant. In reality, however, these functions do vary over time. It is then of practical interest to develop efficient computational algorithms that can deal with time dependent reversion and volatility functions. The purpose of this article is to achieve this goal via the Ehrenfest approximation of the underlying O-U process, where the time dependent structure is represented by step functions. Based on the convergence theorem by Sumita, Gotoh and Jin [2006] and the uniformization procedure of Keilson [1979], a novel approach is proposed to evaluate the prices of zero-coupon discount bonds and associated European options for stepwise reversion and volatility functions. The ordinary Hull-White trinomial tree approach is also modified to cope with this case for comparison purposes. However, it is shown that the modified trinomial tree approach is not applicable for certain step functions, while the Ehrenfest approach can always be used for any step functions. Numerical results are given, demonstrating the excellent speed and accuracy of the Ehrenfest approach.

DOI： 10.3905/jod.2007.694793

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：ELSEVIER SCIENCE BV  

In this paper, we consider the minimization of the conditional value-at-risk (CVaR), a most preferable risk measure in financial risk management, in the context of the well-known single-period newsvendor problem, which is originally formulated as the maximization of the expected profit or the minimization of the expected cost. We show that downside risk measures including the CVaR are tractable in the problem due to their convexity, and consequently, under mild assumptions on the probability distribution of products' demand, we provide analytical solutions or linear programming (LP) formulation of the minimization of the CVaR measures defined with two different loss functions. Numerical examples are also exhibited, clarifying the difference among the models analyzed in this paper, and demonstrating the efficiency of the LP solutions. (c) 2006 Elsevier B.V. All rights reserved.

DOI： 10.1016/j.ejor.2006.03.022

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：Springer  

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：Kluwer Academic Publishers (現:Springer)  

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：日本オペレーションズ・リサーチ学会  

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：Yokohama Publisher  

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：TAYLOR & FRANCIS LTD  

The problem of minimizing the flow value attained by maximal flows plays an important and interesting role to investigate how inefficiently a network can be utilized. It is a typical multiextremal optimization problem, which can have local optima different from global optima. We formulate this problem as a global optimization problem with a special structure and propose a method to combine different techniques in local search and global optimization. Within the proposed algorithm, the advantageous structure of network flow is fully exploited so that the algorithm should be suitable for handling the problem of moderate sizes.

DOI： 10.1080/1055678031000120191

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：INFORMS  

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：Elsevier  

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記述言語：英語   掲載種別：研究論文（国際会議プロシーディングス）   出版者・発行元：SPRINGER  

This paper addresses itself to a new approach for failure discriminant analysis, a classical and yet very actively studied problem in financial engineering. The basic idea of the new method is to separate multi-dimensional financial data corresponding to ongoing and failed enterprises by an ellipsoidal surface which enjoys a good mathematical property as well as a clear financial interpretation.
We will apply a new cutting plane algorithm for solving a resulting semi-definite programming problem and show that it can generate an optimal solution in a much more efficient way than standard interior point algorithms. Computational results using financial data of Japanese enterprises show that the ellipsoidal separation leads to significantly better results than the hyperplane separation. Also it performs better than the separation by a general quadratic surface, a well used method in support vector machine approach.

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：KLUWER ACADEMIC PUBL  

In this paper, we will develop an algorithm for solving a quadratic fractional programming problem which was recently introduced by Lo and MacKinlay to construct a maximal predictability portfolio, a new approach in portfolio analysis. The objective function of this problem is defined by the ratio of two convex quadratic functions, which is a typical global optimization problem with multiple local optima. We will show that a well-designed branch-and-bound algorithm using (i) Dinkelbach's parametric strategy, (ii) linear overestimating function and (iii) omega -subdivision strategy can solve problems of practical size in an efficient way. This algorithm is particularly efficient for Lo-MacKinlay's problem where the associated nonconvex quadratic programming problem has low rank nonconcave property.

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：INST OPERATIONS RESEARCH MANAGEMENT SCIENCES  

In their recent article, Ogryczak and Ruszczynski (1999) proved that those portfolios associated with the efficient frontiers generated by mean-lower semi-standard deviation model and mean- (lower semi-)absolute deviation model are efficient in the sense of second degree stochastic dominance. This rather surprising result reveals the importance of lower partial risk models in portfolio analysis.
In this paper, we extend the results of Ogryczak and Ruszczynski for second degree stochastic dominance to third degree stochastic dominance. We show that portfolios on a significant portion of the efficient frontier generated by mean-lower semi-skewness model are efficient in the sense of third degree stochastic dominance. Also, we prove that the portfolios generated by mean-variance-skewness model are semi-efficient in the sense of third degree stochastic dominance.

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記述言語：日本語   掲載種別：研究論文（学術雑誌）   出版者・発行元：日本金融・証券計量・工学学会  

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記述言語：日本語   掲載種別：研究論文（学術雑誌）   出版者・発行元：日本金融・証券計量・工学学会  

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記述言語：英語   会議種別：口頭発表（一般）  

In this talk we study applications and efficient algorithms for k-sparse recovery problem on the basis of the Continuous Exact k-Sparse Penalties (CXPs) or which is also known as partial regularizers. Each CXP is defined by a non-convex but continuous function and the equality forcing the function value to be zero is known to be equivalent to the k-sparse constraint defined with the so-called l0-norm. Algorithms based on the proximal mapping of the lp-norm based CXPs will be examined for sparsity-seeking estimation problems such as a sparse robust.regression problem.

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記述言語：英語   会議種別：公開講演，セミナー，チュートリアル，講習，講義等  

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記述言語：日本語   会議種別：公開講演，セミナー，チュートリアル，講習，講義等  

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記述言語：英語   会議種別：口頭発表（一般）  

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記述言語：英語   会議種別：公開講演，セミナー，チュートリアル，講習，講義等  

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記述言語：日本語   会議種別：口頭発表（一般）  

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記述言語：英語   会議種別：口頭発表（一般）  

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記述言語：英語   会議種別：口頭発表（一般）  

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記述言語：英語   会議種別：公開講演，セミナー，チュートリアル，講習，講義等  

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記述言語：日本語   会議種別：口頭発表（一般）  

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記述言語：英語   会議種別：口頭発表（一般）  

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記述言語：英語   会議種別：口頭発表（一般）  

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記述言語：日本語   会議種別：口頭発表（一般）  

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記述言語：日本語   会議種別：口頭発表（一般）  

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記述言語：英語   会議種別：口頭発表（一般）  

researchmap

記述言語：英語   会議種別：口頭発表（一般）  

researchmap

記述言語：英語   会議種別：口頭発表（一般）  

researchmap

記述言語：英語   会議種別：口頭発表（一般）  

researchmap

記述言語：日本語   会議種別：口頭発表（一般）  

researchmap

記述言語：日本語   会議種別：口頭発表（一般）  

researchmap