在 mortality shock 下的最优 annuitization 时间
Optimal Annuitization Time under a Mortality Shock
AI总结：
本文研究在突发健康恶化下的最优 annuitization 时间，通过分析投资组合和生命年金的相互作用，揭示健康状态对决策的影响。
摘要：
本文推导了在突发健康恶化下的最优 annuitization 问题中价值函数和相关最优停止边界的确切闭式解。我们考虑一个退休者将其财富投资于遵循几何布朗运动的金融基金，并在任何时候不可逆地将财富转换为生命年金。个体面临一个突然且永久的健康恶化，发生在随机的指数分布时间，annuitization 决策被建模为在两个健康状态之间的最优停止问题。我们的分析表达式刻画了价值函数和 annuitization 的最佳时间。结果提供了清晰的经济直觉：最优策略由年金（货币价值）的相对吸引力、投资基金的财务回报以及不同健康状态下的遗产动机之间的关键相互作用所支配。数值分析比较了面临健康冲击的个体的最优 annuitization 策略与常数死亡率的基准案例，突显了健康冲击的可能性和严重性如何显著改变最优 annuitization 行为。
英文摘要：
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.
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