Time consistent fuzzy multi-period rolling portfolio optimization with adaptive risk aversion factor

Abstract

This study focuses on a time consistent multi-period rolling portfolio optimization problem under fuzzy environment. An adaptive risk aversion factor is first defined to incorporate investor’s changing psychological risk concerns during the intermediate periods. Within the framework of credibility theory, the future returns of risky assets are represented by triangular and trapezoidal fuzzy variables, respectively, which are estimated by utilizing justifiable granularity principle using real financial data from Shanghai stock exchange (SSE). The return and risk of assets at each Investment period are measured by expected value and entropy, respectively. The problem is then formulated by a series of rolling deterministic linear programmings and solved with simplex methods. Numerical examples are provided to illustrate the effectiveness of the proposed adaptive risk aversion factor and rolling formulation methodologies.