Portfolio selection with stochastic volatility and continuous dividends

This paper study the problem of the portfolio selection. It is established that the behavior model of the stock pricing process is jump-diffusion driven by a count process and stochastic volatility. Supposing that risk assets pay continuous dividend regarded as the function of time.It is proved that the existence of an optimal portfolio and unique equivalent martingale measure by stochastic analysis methods. The unique equivalent martingale measure,the optimal wealth process, the value function and the optimal portfolio are deduced.