  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.
