Optimal Annuitization Time under a Mortality Shock

2026-04-10

AI Summary

This study addresses the optimal timing of annuitization for individuals facing a sudden and permanent deterioration in health—modeled as a mortality shock. The decision problem is formulated as an irreversible optimal stopping problem with two health states, assuming retirement wealth is invested in a geometric Brownian motion asset and can be converted at any time into a life annuity. For the first time within a mortality-jump framework, the authors derive explicit analytical solutions for both the value function and the optimal stopping boundary, elucidating the interplay among annuity value-for-money, investment returns, and bequest motives across health states. Integrating stochastic control, dynamic programming, and exponential jump-time modeling, numerical analysis demonstrates that both the probability and severity of health shocks significantly shape annuitization strategies, offering more realistic guidance than models assuming constant mortality rates.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• User Modeling, Personalization and Recommendation: Studies of user behavior, including longitudinal effects of personalized systems
• Web Mining and Content Analysis: Models for Web evolution

Abstract

In this paper, we derive explicit closed-form solutions for the value function and the associated optimal stopping boundaries in an optimal annuitization problem under a mortality shock. We consider an individual whose retirement wealth is invested in a financial fund following the dynamics of a geometric Brownian motion and has the option at any time to irreversibly convert their wealth into a life annuity. The individual faces a sudden, permanent health deterioration occurring at a random, exponentially distributed time, and the annuitization decision is modelled as an optimal stopping problem across two health states. Our analytical expressions characterise both the value function and the optimal timing of annuitization. The results provide clear economic intuition: the optimal strategy is governed by the critical interplay between the relative attractiveness of the annuity (money's worth), the financial returns from the investment fund, and bequest motives across different health states. A numerical analysis compares the optimal annuitization strategy of an individual facing a health shock against a benchmark case with constant mortality, highlighting how the likelihood and severity of a health shock significantly alter optimal annuitization behaviour.

Problem

• optimal annuitization
• mortality shock
• health deterioration
• retirement wealth
• optimal stopping

Innovation

• optimal stopping
• annuitization
• mortality shock
• closed-form solution
• health state