Optimal Consumption and Investment Strategies in a Jump-Diffusion Model

A portfolio optimization problem with consumption is considered.Risky asset price obeys jump-diffusion process, and the dividend is paid continuously.The goal is to choose optimal investment and consumption policies for the problem of maximizing expected total utility form both consumption and terminal wealth. It is fined unique equivalent martingale measure, we employ the conventional stochastic analysis methods. We find explicit formula for the optimal portfolio and the consumption process.In addition, for a special case where the utility is logarithmic or is a power function, an explicit formula is given.