Global optimization for the portfolio selection model with high-order moments

TL;DR

This paper develops a robust global optimization method for polynomial portfolio models with high-order moments, using semidefinite programming and moment relaxations to efficiently approximate optimal solutions.

Contribution

It introduces a perturbation sample average approximation approach combined with Moment-SOS relaxations for solving high-order moment portfolio optimization problems.

Findings

The proposed method provides reliable approximations of the optimal value.

Numerical examples demonstrate the efficiency of the algorithm.

The approach is robust for high-order moment portfolio models.

Abstract

In this paper, we study the global optimality of polynomial portfolio optimization (PPO). The PPO is a kind of portfolio selection model with high-order moments and flexible risk preference parameters. We introduce a perturbation sample average approximation method, which can give a robust approximation of the PPO in form of linear conic optimization. The approximated problem can be solved globally with Moment-SOS relaxations. We summarize a semidefinite algorithm, which can be used to find reliable approximations of the optimal value and optimizer set of the PPO. Numerical examples are given to show the efficiency of the algorithm.