论年金购买的自由边界
On the free boundary of an annuity purchase
摘要：
众所周知，购买年金的决策可能与最优停时问题相关联。然而，很少有人知道最佳战略，如果死亡率是一个通用的功能的时间，如果“主观”预期寿命的投资者不同于“客观”的保险公司采用的价格年金。在本文中，我们解决这个问题，考虑个人谁投资于基金，并有选择转换基金的价值在任何时候到年金。我们制定的问题作为一个真正的选择，并进行详细的概率研究的最优停时的边界。由于死亡力的一般时间依赖性，我们的最优停时问题需要新的解决方法来处理非单调的最优边界。
英文摘要：
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 if 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 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 non-monotonic optimal boundaries.
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