Jump-Diffusion Risk-Sensitive Asset Management

Abstract. This paper considers a portfolio optimization problem in which asset prices are represented by SDEs driven by Brownian motion and a Poisson random measure, with drifts that are functions of an auxiliary diffusion factor process. The criterion, following earlier work by Bielecki, Pliska, Nagai and others, is risk-sensitive optimization (equivalent to maximizing the expected growth rate subject to a constraint on variance.) By using a change of measure technique introduced by Kuroda and Nagai we show that the problem reduces to solving a certain stochastic control problem in the factor process, which has no jumps. The main result of the paper is that the Hamilton-JacobiBellman equation for this problem has a classical (C) solution. The proof uses Bellmans policy improvement method together with results on linear parabolic PDEs due to Ladyzhenskaya et al.