Risk-sensitive investment in a finite-factor model

TL;DR

This paper introduces a jump diffusion regime-switching model linking asset price jumps with regime changes, and provides a numerical method for solving the associated risk-sensitive asset management problem.

Contribution

It develops a new model connecting jumps and regime shifts, proves solution existence and uniqueness, and offers an efficient numerical approach for the optimal control problem.

Findings

Existence and uniqueness of the solution are established.

An ODE for the optimal value function is derived.

Numerical methods for solving the model are proposed.

Abstract

A new jump diffusion regime-switching model is introduced, which allows for linking jumps in asset prices with regime changes. We prove the existence and uniqueness of the solution to the risk-sensitive asset management criterion maximisation problem in this setting. We provide an ODE for the optimal value function, which may be efficiently solved numerically. Relevant probability measure changes are discussed in the appendix. The approach of Klebaner and Lipster (2014) is used to prove the martingale property of the relevant density processes.