老龄化债券在累积和分配阶段的固定缴款养老金中的作用  

The Role of Longevity Bond in DC Pension Plan During Both Accumulation and Decumulation Phases

作　　者：张笑怡 ZHANG Xiao-yi(School of Economics and Management,Hebei University of Technology,Tianjin 300401)

机构地区：[1]河北工业大学经济管理学院,天津300401

出　　处：《工程数学学报》2020年第3期347-369,共23页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(11571189);中央高校基本科研业务费专项资金(63185019).

摘　　要：近年来,老龄化风险在金融数学和金融工程领域引起了人们极大的关注.为了对冲老龄化风险,老龄化债券在金融市场上应运而生.为了研究老龄化债券是否能有效地对冲固定缴款养老金账户所面临的老龄化风险,本文分别对累积阶段和分配阶段的固定缴款养老金进行了随机最优管理问题的研究.在两个阶段中,最优控制的目标都是通过对金融市场上老龄化债券、零息票债券和无风险资产的投资来最大化终端财富值的期望效用.应用动态规划原理并通过解相应的HJB方程,本文分别得到了两个阶段的最优投资策略的显式表达.在合理的假设前提下,结果表明无论是在累积阶段还是在分配阶段,对老龄化债券的投资都有利于提高投资效果,并最终得到更高的财富值的期望效用.Longevity risk has attracted increasing attention in financial mathematics and financial engineering area.Longevity bond is defined as a kind of financial instrument to hedge longevity risk.To investigate whether the longevity bond can hedge longevity risk in defined contribution(DC)pension plans effectively,this paper deals with two optimal management problems for a DC pension plan during its accumulation phase and decumulation phase,respectively.For both problems,the scheme aims to maximize the expected constant relative risk aversion(CRRA)utility from the terminal fund by investing its wealth in a financial market consisting of a longevity bond and a risk-free asset.Closed-form optimal investment strategies are derived by using the dynamic programming approach and solving the related HJB equation.Under rational assumptions,the results reveal that the maximal expected utility under the market with a longevity bond is higher than the maximal expected utility under the market with an ordinary bond,in both phases.

关 键 词：老龄化风险 老龄化债券 固定缴款养老金 随机最优控制 HJB方程 

分 类 号：O211.9[理学—概率论与数理统计]