Jump-Diffusion Risk-Sensitive Asset Management II: Jump-Diffusion Factor Model

TL;DR

This paper extends jump-diffusion risk-sensitive asset management models by incorporating jumps in factors and asset prices, stochastic volatility, and constraints, and proves the existence of a unique smooth solution to the resulting complex HJB PIDE.

Contribution

It introduces a comprehensive framework for jump-diffusion models with stochastic volatility and constraints, proving the existence and uniqueness of solutions to the associated HJB PIDE.

Findings

Proves the HJB PIDE admits a unique smooth solution.

Extends previous models to include jumps in factors and prices.

Provides a verification theorem for the control problem.

Abstract

In this article we extend earlier work on the jump-diffusion risk-sensitive asset management problem [SIAM J. Fin. Math. (2011) 22-54] by allowing jumps in both the factor process and the asset prices, as well as stochastic volatility and investment constraints. In this case, the HJB equation is a partial integro-differential equation (PIDE). By combining viscosity solutions with a change of notation, a policy improvement argument and classical results on parabolic PDEs we prove that the HJB PIDE admits a unique smooth solution. A verification theorem concludes the resolution of this problem.