Life insurance completeness : a path to hedging mortality and achieving financial optimization

This paper explores optimal consumption and investment strategies for agents facing mortality risk within a complete financial market. Departing from traditional frameworks, we leverage state-dependent utility theory, discounted by the state-price process, to compare consumption streams and utilize life insurance as a strategic hedging instrument. To model the ability of insurance companies to hedge the mortality risk of consumer pools, we introduce the concept of life insurance completeness, allowing individuals to achieve optimal consumption even in scenarios involving negative wealth. Our model relaxes the stringent integrability conditions commonly imposed in the literature, offering a more economically grounded approach to valuation and hedging. We derive a general solution to the optimization problem using martingale techniques under minimal assumptions, demonstrating that life insurance primarily serves as a mortality risk hedge rather than a bequest motive. This perspective resolves longstanding theoretical and empirical challenges, notably the annuity puzzle, by illustrating that optimal consumption and investment, in the absence of labor income, do not necessitate annuities or other life insurance policies. Our key contributions include (1) extending valuation frameworks to encompass prepaid insurance and less restrictive integrability criteria, (2) establishing life insurance completeness for effective mortality risk hedging, (3) demonstrating the feasibility of optimal consumption under negative wealth and state-dependent preferences, and (4) offering a resolution to the annuity puzzle that aligns with empirical observations.