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

This paper studies four families of polyhedral norms parametrized by a single parameter. The first two families consist of the CVaR norm (which is equivalent to the D-norm, or the largest- norm) and its dual norm, while the second two families consist of the convex combination of the - and -norms, referred to as the deltoidal norm, and its dual norm. These families contain the - and -norms as special limiting cases. These norms can be represented using linear programming (LP) and the size of LP formulations is independent of the norm parameters. The purpose of this paper is to establish a relation of the considered LP-representable norms to the -norm and to demonstrate their potential in optimization. On the basis of the ratio of the tight lower and upper bounds of the ratio of two norms, we show that in each dual pair, the primal and dual norms can equivalently well approximate the - and -norms, respectively, for satisfying . In addition, the deltoidal norm and its dual norm are shown to have better proximity to the -norm than the CVaR norm and its dual. Numerical examples demonstrate that LP solutions with optimized parameters attain better approximation of the -norm than the - and -norms do.

DOI： 10.1007/s10107-015-0899-9

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：Taylor \& Francis  

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

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：INST OPERATIONS RESEARCH MANAGEMENT SCIENCES  

In a recent article, Bertsimas and Popescu showed that a tight upper bound on a European-type call option price, given the first n moments of the distribution of the underlying security price, can be obtained by solving an associated semidefinite programming problem (SDP). The purpose of this paper is to improve and extend their results. We will show that a tight lower bound can be calculated by solving another SDP. Also, we will show that these problems can be solved very quickly by a newly developed cutting plane algorithm when n is less than six or seven.

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

DOI： 10.1007/s13160-023-00631-5

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Other Link： https://link.springer.com/article/10.1007/s13160-023-00631-5/fulltext.html

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DOI： 10.1016/j.orp.2022.100262

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

DOI： 10.1007/s11590-021-01716-1

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

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

This paper studies the peer-to-peer lending and loan application processing of LendingClub. We tried to reproduce the existing loan application processing algorithm and find features used in this process. Loan application processing is considered a binary classification problem. We used the area under the ROC curve (AUC) for evaluation of algorithms. Features were transformed with splines for improving the performance of algorithms. We considered three classification algorithms: logistic regression, buffered AUC (bAUC) maximization, and AUC maximization.With only three features, Debt-to-Income Ratio, Employment Length, and Risk Score, we obtained an AUC close to 1. We have done both in-sample and out-of-sample evaluations. The codes for cross-validation and solving problems in a Portfolio Safeguard (PSG) format are in the Appendix. The calculation results with the data and codes are posted on the website and are available for downloading.

DOI： 10.3390/risks6040129

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DOI： 10.1007/s10479-017-2749-z

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Language：English   Publishing type：Part of collection (book)   Publisher：wiley  

This chapter overview the connections between support vector machines (SVM) and conditional value at risk (CVaR) minimization and suggests further interactions beyond their similarity in appearance. It introduces several SVM formulations, whose relation to CVaR minimization. The chapter further discusses robust extensions of the CVaR formulation. It presents the dual problems of the CVaR-minimizing formulations, and shows that two kinds of robust modeling of the CVaR minimization for binary classification are tractable. Dual representations expand the range of algorithms and enrich the theory of SVM. SVMs are one of the most successful supervised learning methods that can be applied to classification or regression. The maximum margin hyperplane of hard-margin SVM classification (SVC) minimizes an upper bound of the generalization error. The support vector regression (SVR) method performs well in regression analysis and is a popular data analysis tool in machine learning and signal processing.

DOI： 10.1002/9781118745540.ch10

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Language：Japanese   Publishing type：Research paper (scientific journal)   Publisher：朝倉書店  

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

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

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：SPRINGER/PLENUM PUBLISHERS  

We generalize the notion of arbitrage based on the coherent risk measure, and investigate a mathematical optimization approach for tightening the lower and upper bounds of the price of contingent claims in incomplete markets. Due to the dual representation of coherent risk measures, the lower and upper bounds of price are located by solving a pair of semi-infinite linear optimization problems, which further reduce to linear optimization when conditional value-at-risk (CVaR) is used as risk measure. We also show that the hedging portfolio problem is viewed as a robust optimization problem. Tuning the parameter of the risk measure, we demonstrate by numerical examples that the two bounds approach to each other and converge to a price that is fair in the sense that seller and buyer face the same amount of risk.

DOI： 10.1007/s10957-011-9899-y

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Language：Japanese   Publishing type：Research paper (scientific journal)   Publisher：日本オペレーションズ・リサーチ学会  

Credit risk is the risk of loss stemming from borrower's default. We consider the credit risk minimization problem and propose an optimization method for minimizing the risk measured by Conditional Value-at-Risk (CVaR) criterion. Default of firms is modeled by the corporate valuation model and the factor analysis of time series data of TOPIX Sector Indices, scenarios of defaults are generated, and then CVaR minimization problem is solved. By varying the number of factors incorporated in the model as well as the coefficient that determines the impact of factors peculiar to industry type, we observe how economic trend, industry type and rating of the firms influence the defaults and the credit risk. A large number of scenarios are required to obtain a reliable implication; however, the CVaR minimization problem becomes harder to solve. We propose a simple but effective pre-treatment of the scenarios and also a solution technique. We solved the problem with a hundred thousand scenarios in about 7 seconds and that with half a million scenarios in about 35 seconds.

DOI： 10.15807/torsj.54.23

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：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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Language：English   Publishing type：Research paper (scientific journal)   Publisher：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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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：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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Language：English   Publishing type：Research paper (scientific journal)   Publisher：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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Language：English   Publishing type：Research paper (international conference proceedings)  

Support vector regression (SVR) is a popular regression algorithm in machine learning and signal processing. In this paper, we first prove that the SVR algorithm is equivalent to minimizing the conditional value-at-risk (CVaR) of the distribution of the ℓ1-loss residuals, which is a popular risk measure in finance. The equivalence between SVR and CVaR minimization allows us to derive a new upper bound on the ℓ1-loss generalization error of SVR. Then we show that SVR actually minimizes the upper bound under some condition, implying its optimality. We finally apply the SVR method to an index tracking problem in finance, and develop a new portfolio selection method. Experiments show that the proposed method compares favorably with alternative approaches. ©2010 IEEE.

DOI： 10.1109/MLSP.2010.5589245

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

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：The Operations Research Society of Japan  

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

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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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Language：Japanese   Publishing type：Research paper (scientific journal)   Publisher：日本金融・証券計量・工学学会  

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Language：Japanese   Publishing type：Research paper (scientific journal)   Publisher：日本金融・証券計量・工学学会  

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Language：Japanese   Publisher：公益社団法人日本オペレーションズ・リサーチ学会  

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Language：Japanese   Publisher：公益社団法人日本オペレーションズ・リサーチ学会  

本稿では「機械学習」と「金融工学」という,独立に生まれ,発展してきた2つの分野の方法論に共通する構造と差異に着目して,新しい発見に繋げようという試みを紹介したい.とりわけ,「機械学習」と「金融工学」の間では双方向への貢献が可能であること,そして両分野間に素敵な関係を見いだすことができることを示す.

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Language：Japanese   Publisher：日本オペレーションズ・リサーチ学会  

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Language：Japanese   Publisher：京都大学  

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Other Link： http://hdl.handle.net/2433/58868

Language：Japanese   Publisher：公益社団法人日本オペレーションズ・リサーチ学会  

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Language：English   Publishing type：Article, review, commentary, editorial, etc. (other)   Publisher：筑波大学システム情報工学研究科社会システム・マネジメント専攻  

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記事種別: 会議・学会報告・シンポジウム

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Language：Japanese   Publishing type：Article, review, commentary, editorial, etc. (other)   Publisher：朝倉書店  

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記事種別: 会議・学会報告・シンポジウム

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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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Language：English   Presentation type：Oral presentation (general)  

researchmap

Language：Japanese   Presentation type：Oral presentation (general)  

researchmap

Language：English   Presentation type：Oral presentation (general)  

researchmap

Language：English   Presentation type：Oral presentation (general)  

researchmap

Language：English   Presentation type：Oral presentation (general)  

researchmap

Language：English   Presentation type：Oral presentation (general)  

researchmap

Language：English   Presentation type：Oral presentation (general)  

researchmap

Language：English   Presentation type：Oral presentation (general)  

researchmap

Language：English   Presentation type：Oral presentation (general)  

researchmap

Language：Japanese   Presentation type：Oral presentation (general)  

researchmap

Language：English   Presentation type：Oral presentation (general)  

researchmap

Language：English   Presentation type：Oral presentation (general)  

researchmap

Language：Japanese   Presentation type：Oral presentation (general)  

researchmap

Language：English   Presentation type：Oral presentation (general)  

researchmap

Language：Japanese   Presentation type：Oral presentation (general)  

researchmap

Language：Japanese   Presentation type：Oral presentation (general)  

researchmap

Language：English   Presentation type：Oral presentation (general)  

researchmap

Language：English   Presentation type：Oral presentation (general)  

researchmap

Language：English   Presentation type：Oral presentation (general)  

researchmap

Language：English   Presentation type：Oral presentation (general)  

researchmap

Language：English   Presentation type：Oral presentation (general)  

researchmap

Language：English   Presentation type：Oral presentation (general)  

researchmap

Language：English   Presentation type：Oral presentation (general)  

researchmap

Language：English   Presentation type：Oral presentation (general)  

researchmap

Language：English   Presentation type：Oral presentation (general)  

researchmap

Language：English   Presentation type：Oral presentation (general)  

researchmap

Language：English   Presentation type：Oral presentation (general)  

researchmap

Language：English   Presentation type：Oral presentation (general)  

researchmap

Language：Japanese   Presentation type：Oral presentation (general)  

researchmap

Language：Japanese   Presentation type：Oral presentation (general)  

researchmap