An incremental bundle method for portfolio selection problem under second-order stochastic dominance

Abstract

In this paper, we propose an incremental bundle method with inexact oracle for solving the portfolio optimization with stochastic second-order dominance (SSD) constraints. We first relax the SSD problem as a stochastic semi-infinite programming (SIP) problem. For the particular case of SIP problem, we exploit the improvement function and the idea of incremental technique for dealing with the infinitely many constraints. In the stochastic model, as an adding-rules, the “inexact oracle” is introduced in this algorithm. Therefore, the algorithm does not need all the information about the constraints, but only needs the inexact information of one component function to update the bundle and produces the search direction. Our numerical results on solving the academic problems have shown advantages of the incremental bundle method over three existing algorithms. Finally, numerical results on a part of portfolio optimization problem are presented by using the FTSE100 Index.