  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 to show that the risk-sensitive jump diffusion
problem can be fully characterized in terms of a parabolic
Hamilton-Jacobi-Bellman PDE rather than a PIDE, and that this PDE admits a
classical C^{1,2} solution.
