一类含消费、寿险和投资的随机最优控制问题

Optimal investment, consumption and life insurance under stochastic framework

本文研究在CRRA(constant relative risk aversion)效用下,关于消费、寿险和投资的随机最优控制问题.投资者可以投资于零息债券、股票和寿险.假设利率模型是Vasicek模型,股票模型是广义Heston随机波动率模型.此外,用Black-Scholes模型刻画收入项,且收入的增长率与利率有协整关系.通过动态规划的方法和解对应的HJB(Hamilton-Jacobi-Bellman)方程的技术得到最优策略.为了探索各个经济参数对最优策略的影响,本文给出数值分析.

In this paper, we consider an optimal control problem of investment, consumption and life insurance for a wage earner who has constant relative risk aversion （CRRA） preferences. The wage earner can invest in zero-coupon bond, stock and life insurance. The interest rate is Vasicek model, the stock follows an extension of Heston stochastic volatility model. We use a generalized Black-Scholes model to characterize labor income. Risks of the income＇s increasing rate and interest rate are cointegrated. The optimal strategies of the problem are derived by dynamic programming method and technique of solving associated HJB equations. We also present a sensitivity analysis to explore the impact of economical parameters on the optimal strategies.