An optimal life insurance policy in the continuous-time investment – consumption problem

Abstract

This paper considers an optimal life insurance purchase for a household subject to mortality risk. The household receives wage income continuously, which could be terminated by unexpected premature loss of earning power. In order to hedge the risk of losing income stream, the household enters a life insurance contract for the bereft members. The household may also invest their wealth into a financial market. If insurance payment is made prior to the planned time horizon, the amount shall be used for consumption and investment. Therefore, the problem is to determine an optimal insurance/investment/consumption strategy in order to maximize the expected total discounted utility from consumption and terminal wealth. We provide explicit solutions in a fairly general setup.