Optimal investment, consumption and life insurance purchase with learning about return predictability

Abstract

This paper studies the optimal investment, consumption and life insurance purchase problem for a wage earner under the condition that the return on the risky asset is predictable. We assume that the market price of risk is an affine function consisting of an observable and an unobservable factor that follow the O-U processes, while the evolution of the interest rate is described by the Vasicek model. The optimal investment, consumption and life insurance strategies and the corresponding value function are derived by adopting the filtering technique and the dynamical programming principle approach. In addition, for comparative analysis, the suboptimal strategies and the utility losses are presented when the wage earner ignores learning or the randomness of the interest rate. Finally, some numerical examples are presented to illustrate the results.