Optimal portfolio and consumption under pure jump process

The aim of this paper is to assess the impact of jumps in the asset returns dynamics on the optimal portfolio and consumption problem. We consider an investor who wants to maximize his utility from consumption and who is placing his money into stocks and a money market. His utility is given by a power utility function. In this paper, we present equations for the optimal consumption and portfolio choice. We also introduce an alternative equations for the optimal values in terms of cumulants. Using these new equations we discuss the effect of skewness and kurtosis on the optimal investment strategy and consumption. Finally, we perform a numerical study.