Portfolio Optimization on Jump Diffusion
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Portfolio optimization problem is an important research topic in financial applications. In this research, we focus on a consumption process and a terminal wealth problem. A portfolio including a riskless asset, a zero coupon bond and a stock is presented. All assets are modeled by continuous time dynamic. Bond is modeled by a classical Vasicek’s model. A stock is modeled using Merton Jump diffusion (MJD) model. This work is new because an economic inflation rate and consumption price index (CPI) are taken into consideration to evaluate a real value of assets. A Hamilton-Jacobi-Bellman (HJB) equation that satisfies an optimal solution is derived. Then, the solution is proved to exist and to be unique under certain conditions. Finally, the solution is found by using numerical method.