带跳分数布朗运动下最优金融决策

Under the hypothesis that asset price follow a fractional Brownian motion with Poisson jump, a class of optimal portfolio and consumption problem that combines life insurance is studied in the present paper. Based on the criterion of maximizing the investor's expected utility in the life cycle of investment, consumption and insurance, the optimal investment and consumption choice model was established using dynamic programming principle. The optimal analytic solutions of the optimal financial approach were obtained by solving the HJB equation under the CRRA utility function.