基于通货膨胀和最低保障的DC养老金最优投资

doi:10.12005/orms.2018.0052

运筹与管理 ›› 2018, Vol. 27 ›› Issue (2): 193-199.DOI: 10.12005/orms.2018.0052

• 管理科学 • 上一篇

基于通货膨胀和最低保障的DC养老金最优投资

王传玉, 付春艳, 盛国祥

安徽工程大学数理学院,安徽芜湖 241000

收稿日期:2017-08-11 出版日期:2018-02-25
作者简介:王传玉(1964-),男,教授,硕士生导师,研究方向为精算数学;付春艳(1994-),通讯作者,女,硕士研究生,研究方向为金融数学与金融工程;盛国祥(1993-),男,硕士研究生,研究方向为金融数学与金融工程。
基金资助:
国家自然科学基金资助项目(61503001)

Optimal Investment of DC Pension under the Inflation and Minimum Guarantee

WANG Chuan-yu, FU Chun-yan, SHENG Guo-xiang

Department of Financial Engineering, Anhui Polytechnic University, Wuhu 241000, China

Received:2017-08-11 Online:2018-02-25

摘要/Abstract

摘要： 主要研究了通货膨胀和最低保障下的DC养老金的最优投资问题。首先, 应用伊藤公式得到通胀折现后真实股票价格的微分方程。然后, 在DC养老金终端财富外部保障约束下, 引入欧式看涨期权, 考虑随机通胀环境下的退休时刻终端财富期望效用最大化问题, 应用鞅方法推导退休时刻以及退休前任意时刻DC养老金最优投资策略的显式解。最后, 应用蒙特卡洛方法对结果进行数值分析, 分析最低保障对DC养老金最优投资策略的影响。

关键词: 通货膨胀, 最低保障, DC养老金, 最优投资, 鞅方法

Abstract: This paper mainly studies the optimal investment problem of DC pension under the inflation and minimum guarantee. First, we use the Ito formula to derive the stochastic differential equation for the real stock price discounted by inflation. And then, introducing European call options and considering the problem of maximizing the expected utility of terminal wealth discounted by inflation at retirement under the minimum guarantee, we use the martingale method to derive the explicit solution of the optimal investment strategy of DC pension at retirement and any time before retirement. In the end, we analyze the impact of the minimum guarantee on the optimal investment strategy of DC pension through using the Monte-Carlo method.

Key words: inflation, minimum guarantee, DC pension, optimal investment, martingale method

中图分类号:

F832.48

王传玉, 付春艳, 盛国祥. 基于通货膨胀和最低保障的DC养老金最优投资[J]. 运筹与管理, 2018, 27(2): 193-199.

WANG Chuan-yu, FU Chun-yan, SHENG Guo-xiang. Optimal Investment of DC Pension under the Inflation and Minimum Guarantee[J]. Operations Research and Management Science, 2018, 27(2): 193-199.

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基于通货膨胀和最低保障的DC养老金最优投资

Optimal Investment of DC Pension under the Inflation and Minimum Guarantee

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