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Interaction between financial risk measures and machine learning methods

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Abstract

The purpose of this article is to review the similarity and difference between financial risk minimization and a class of machine learning methods known as support vector machines, which were independently developed. By recognizing their common features, we can understand them in a unified mathematical framework. On the other hand, by recognizing their difference, we can develop new methods. In particular, employing the coherent measures of risk, we develop a generalized criterion for two-class classification. It includes existing criteria, such as the margin maximization and \(\nu \)-SVM, as special cases. This extension can also be applied to the other type of machine learning methods such as multi-class classification, regression and outlier detection. Although the new criterion is first formulated as a nonconvex optimization, it results in a convex optimization by employing the nonnegative \(\ell _1\)-regularization. Numerical examples demonstrate how the developed methods work for bond rating.

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Authors and Affiliations

  1. Department of Industrial and Systems Engineering, Chuo University, 2-13-27 Kasuga, Bunkyo-ku, Tokyo, 112-8551, Japan

    Jun-ya Gotoh

  2. Department of Mathematical Informatics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-8656, Japan

    Akiko Takeda

  3. Mitsubishi UFJ Trust Investment Technology Institute Co., Ltd., 4-2-6 Akasaka, Minato-ku, Tokyo, 107-0052, Japan

    Rei Yamamoto

Authors
  1. Jun-ya Gotoh
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  2. Akiko Takeda
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  3. Rei Yamamoto
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Corresponding author

Correspondence to Jun-ya Gotoh.

Additional information

The research of the first author is partly supported by a MEXT Grant-in-Aid for Young Scientists (B) 23710176. Also, the authors appreciate the comments by two anonymous referees and Dr. Pando G. Georgiev.

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Gotoh, Jy., Takeda, A. & Yamamoto, R. Interaction between financial risk measures and machine learning methods. Comput Manag Sci 11, 365–402 (2014). https://doi.org/10.1007/s10287-013-0175-5

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