Robust equilibrium strategy for mean-variance-skewness portfolio selection problem

TL;DR

This paper develops a robust, time-consistent portfolio selection strategy considering mean, variance, skewness, and model uncertainty, providing semi-closed form solutions and numerical insights for ambiguity-averse investors.

Contribution

It introduces a novel robust equilibrium strategy for mean-variance-skewness portfolio optimization under model uncertainty using a game theoretic approach.

Findings

Semi-closed form solutions for the robust strategy

Numerical experiments reveal utility losses and strategy characteristics

New insights into ambiguity-averse portfolio management

Abstract

This paper considers a robust time-consistent mean-variance-skewness portfolio selection problem for an ambiguity-averse investor by taking into account wealth-dependent risk aversion and wealth-dependent skewness preference as well as model uncertainty. The robust equilibrium investment strategy and corresponding equilibrium value function are characterized for such a problem by employing an extended Hamilton-Jacobi-Bellman-Isaacs (HJBI) system via a game theoretic approach. Furthermore, the robust equilibrium investment strategy and corresponding equilibrium value function are obtained in semi-closed form for a special robust time-consistent mean-variance-skewness portfolio selection problem. Finally, some numerical experiments are provided to indicate several new findings concerned with the robust equilibrium investment strategy and the utility losses.