带跳分数布朗运动下最优金融决策

An optimal financial approach under the fractional Brownian model with poisson jump

为了考虑一类带有人寿保险的最优投资消费策略问题,假定风险资产价格过程服从带泊松跳的分数布朗运动,在最大化投资者生命周期内的投资、消费和投保的期望效用的准则下,使用动态规划原理建立了最优投资消费选择模型.最后在CRRA效用下通过求解HJB方程得到了最优金融决策的解析式解.

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.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.