Optimal portfolio and consumption with habit formation in a jump diffusion market

This paper studies optimal portfolio and consumption selection with habit formation in a jump diffusions incomplete market in continuous-time. The stochastic maximum principle for jump processes is applied to solve habit-forming utility maximization problem. We transform this problem into the case not involving habit formation in mechanically. Then the solution in the state feedback form is given. The relationship between maximum principle and dynamic programming is employed to get the expression of the relative risk aversion (RRA) coefficient and its distribution. Finally, for a special case, the stationary mean of the RRA coefficient is obtained and the numerical experiment indicates our model with jump diffusions is better than the model in [1] to resolve the equity premium puzzle in a way.