It is known that the decision to purchase an annuity may be associated to an optimal stopping problem. However, little is known about optimal strategies if the mortality force is a generic function of time and the subjective life expectancy of the investor differs from the objective one adopted by insurance companies to price annuities. In this paper, we address this problem by considering an individual who invests in a fund and has the option to convert the fund’s value into an annuity at any time. We formulate the problem as a real option and perform a detailed probabilistic study of the optimal stopping boundary. Due to the generic time-dependence of the mortality force, our optimal stopping problem requires new solution methods to deal with nonmonotonic optimal boundaries.

中文翻译：

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在年金购买的自由边界上

众所周知，购买年金的决定可能与最佳停止问题相关。但是，如果死亡率是时间的一般函数，并且投资者的主观预期寿命不同于保险公司对年金定价的目标，那么最优策略知之甚少。在本文中，我们通过考虑投资某基金的个人并可以随时将其价值转换为年金的选项来解决此问题。我们将问题公式化为实际选择，并对最佳停止边界进行详细的概率研究。由于死亡率的一般时间依赖性，我们的最优停车问题需要新的求解方法来处理非单调最优边界。