Optimal Portfolio Investment/Consumption in Pure-Jump Processes with Higher Moments‎: ‎A New Approach

‎Continuous-time portfolio optimization in markets having realistic features is a challenging problem in computational finance‎. ‎In this paper‎, ‎we consider optimal portfolio investment-consumption problem in a market with a riskless bond and a single risky asset which is modeled by a pure jump L\ {e}vy process‎. ‎We extend the work presented in [J‎. ‎Cvitani\ {c}‎, ‎V‎. ‎Polimenis and F‎. ‎Zapatero‎, ‎Optimal portfolio allocation with higher moments‎, ‎\newblock {\em Annals of Finance} 4 (2008) 1--28] first by incorporating a consumption component in this model and then presenting the analytic formulas for optimal portfolio allocation and consumption rate for investors having different utility functions including CRRA and CARA‎. ‎Some computational experiments are presented to confirm the theoretical findings in this paper‎.