一类路径依赖型养老金的定价分析/Valuation of A Type of Path-dependent Pension Scheme

2018-09-20 08:12:27

定价 pension 养老金 dependent 依赖型



路径依赖型(Path-dependent)养老金的受益是相当复杂的不确定权益,生存受益与死亡受益均依赖于工资水平的历史路径(若再复杂一些,还可以依赖于投资帐户价值),其定价问题已经超出了传统精算方法的范畴,而更类似于金融衍生品定价。本文利用金融经济学中的不确定权益定价方法对这种类型的养老金进行定价分析。

文章首先对养老金定价问题作一个简单的介绍,并提出了路径依赖型养老金的背景与假设条件,讨论了这种保险产品的金融意义。

然后使用偏微分方程来处理路径依赖型养老金定价问题。在第二章中,在利率为常数的假设下,归结出一个包含两维空间变量的定价方程。再利用相似解化简方法,对此定价模型进行降维处理,并导出边界条件,进而使用有限差分法求出方程的数值解。在第三章中,在利率为随机的假设下,归结出一个包含三维空间变量的定价方程,并对此模型作一些初步分析。在文章的最后一部分,结合近年来较为流行的GOB(Greater of Benefit)型养老金,提出路径依赖型GOB养老金的定价模型,并提出了一些值得探讨的问题。



The benefits promised by path-dependent pension schemes, are rather complex contingent claims. Because benefits of this
type depend on the history of salary, their valuation are beyond the domain of traditional actuarial methods. This paper is to value, on an individual basis, such a pension by applying the contingent claims valuation approach.

First, we introduce the development of pension-pricing problems, then, we give the background and basic assumptions about path-dependent pension schemes, and discuss the virtues of this product.

Then, we will solve the problems with PDE approach. In chapter 2, we assume the interest rate is constant and obtain a pricing PDE with two space variables. After that, we use similarity reduction to get a simple PDE with only one space variable and its boundary conditions. And we use the finite difference method to solve it. In chapter 3, we assume the interest rate is stochastic instead and obtain a pricing PDE with three space variables. And
we do some elementary analysis for it.

In the end, we deduce path-dependent GOB pension schemes combined with popular financial product -- GOB pension schemes, and put forward some challenging problems for further research.