A New Support Vector Machine Model Based on the Discrete Conditional Value-at-Risk

This paper studies a discrete conditional value-at-risk (DCVaR) model with multiple losses based on weight and present a new support vector machine model. We introduce the concept of alpha-CVaR for the case of multiple losses with discrete random variable under the confidence level vector alpha. The alpha-CVaR indicates the conditional expected losses corresponding to the alpha-VaR. The problem of solving the minimal alpha-CVaR results in a nonlinear optimal problem (CVaR), which it is difficult to solve it. In order to get optimal solutions of the (CVaR), we introduce another optimal problem (FCVaR) based on weight and show that the optimal solutions of the (FCVaR) is replace with the solutions of (CVaR). According to the discrete conditional value-at-risk model, we present a new support vector machine model, which is a linear programming problem.