This article studies a portfolio optimization problem, where the market consisting of several stocks is modeled by a multidimensional 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 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.