Financial Signal Processing and Machine Learning

Chapter 10CVaR Minimizations in Support Vector Machines

Jun-ya Gotoh¹ and Akiko Takeda²

¹Chuo University, Japan

²The University of Tokyo, Japan

How to measure the riskiness of a random variable has been a major concern of financial risk management. Among the many possible measures, conditional value at risk (CVaR) is viewed as a promising functional for capturing the characteristics of the distribution of a random variable. CVaR has attractive theoretical properties, and its minimization with respect to involved parameters is often tractable. In portfolio selection especially, the minimization of the empirical CVaR is a linear program. On the other hand, machine learning is based on the so-called regularized empirical risk minimization, where a surrogate of the empirical error defined over the in-sample data is minimized under some regularization of the parameters involved. Considering that both theories deal with empirical risk minimization, it is natural to look at their interaction. In fact, a variant of support vector machine (SVM) known as -SVM implicitly carries out a certain CVaR minimization, though the relation to CVaR is not clarified at the time of the invention of -SVM.

This chapter overviews the connections between SVMs and CVaR minimization and suggests further interactions ...