Risk Sensitive Portfolio Optimization in a Jump Diffusion Model with Regimes

TL;DR

This paper addresses risk-sensitive portfolio optimization in a complex jump-diffusion market model with regimes, establishing theoretical results and numerical methods for finite horizon investment strategies.

Contribution

It introduces a probabilistic approach to solve the HJB equation in a jump-diffusion regime-switching model, ensuring existence and uniqueness of solutions.

Findings

Numerical scheme effectively explores solution behavior under various parameters.

Risk aversion impacts optimal portfolio strategies significantly.

Model captures market jumps and regime changes for realistic portfolio optimization.

Abstract

This article studies a portfolio optimization problem, where the market consisting of several stocks is modeled by a multi-dimensional jump-diffusion process with age-dependent semi-Markov modulated coefficients. We study risk sensitive portfolio optimization on the finite time horizon. We study the problem by using a probabilistic approach to establish the existence and uniqueness of the classical solution to the corresponding Hamilton-Jacobi-Bellman (HJB) equation. We also implement a numerical scheme to investigate the behavior of solutions for different values of the initial portfolio wealth, the maturity, and the risk of aversion parameter.