Optimal investment, consumption and life insurance under stochastic framework

Abstract

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 incomes 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.