Life-cycle model with subsistence consumption constraint and state-dependent utilities

Abstract

This paper studies optimal decision-making for investment, consumption and life insurance with state-dependent utilities in continuous time. It is supposed that an economic agent has a subsistence consumption constraint and an uncertain lifetime horizon. The martingale approach coupled with duality theory has been employed to study the stochastic optimization problem of the economic agent. Specifically, the original optimization problem is transformed into a dual maximization problem involving a system of linear equations. Optimal strategies for investment, consumption and life-insurance purchases are obtained by maximizing the expected discounted utilities from intertemporal consumption, legacy and terminal wealth. Economic insights that may be gained from the solution to the problem are illustrated through numerical examples and case studies based on real data. Specifically, for the real-data case studies, an attention is given to studying the impacts of Covid 19 and the recent inflation on optimal strategies for consumption, investment and life-insurance purchases implied by the solution of our proposed model.