Before revision:  In particular, we consider a portfolio optimization problem, without any consumption and transaction cost, where the market consisting of stock prices is modelled by a multi dimensional jump diffusion process with  semi-Markov modulated coefficients.
After revision:  In particular, we consider a portfolio optimization problem, without any consumption and transaction cost, where the market consisting of several stocks is modeled by a multi-dimensional jump diffusion process with semi-Markov modulated coefficients.