随机环境下带有最低收益保障的DC型养老金

发布时间：2018-02-28 09:37

本文关键词： DC型养老金仿射利率模型 Heston模型最优投资策略指数效用对数效用勒让德变换对偶理论　出处：《天津工业大学》2017年硕士论文　论文类型：学位论文

【摘要】：养老金制度是为社会成员提供养老金的社会化制度,分为两种基本类型:确定给付(DB)型和确定缴费(DC)型.对于DB型养老金,养老金受益额由基金管理者提前确定,为维持养老金平衡,缴费率可随时调整,相关金融风险由基金管理者承担.而对于DC型养老金,缴费率是提前确定的,给付额的多少依赖于养老金的投资回报率,相关的金融风险由投保人承担.随着人口演化以及资本市场的发展,DC型老金在社会保障体系中扮演越来越重要的角色.由于DC型养老金计划投保人必须面临市场风险,未来的退休给付无法得到保障,因此带有最低收益保障的DC型养老金计划已经引起很多研究者的关注,并且在资产投资的利率和波动率都是随机的条件下,对最优投资策略进行讨论研究是非常有必要的.根据金融市场的现况,投资者可以将资金投资于现金、零息债券和股票.本文对随机利率和随机波动率模型下带有最低收益保障的DC型养老金投资问题进行了研究.首先在第一章介绍了 DC型养老金的金融市场和最优投资策略问题的主要研究现状.第二章为本文的预备知识,第三章介绍了本文的金融市场并引入了最低收益保障问题,首先动态规划原理得到了指数效用函数下最优投资策略的显性解,其次应用勒让德变换和对偶理论得到了对数效用下最优投资策略的显性表达式,并分别给出数值算例分析了市场参数分别在指数效用和对数效用函数下对最优投资策略的影响.第四章给出文章的结论与展望,存在的不足和今后要深入研究的方向.
[Abstract]:The pension system is a socialized system that provides pensions to members of society and is divided into two basic types: the defined-benefit (DBB) and the defined-contribution (DC-based). For the DB pension, the pension benefit is determined in advance by the fund manager. In order to maintain the balance of the pension, the contribution rate can be adjusted at any time, and the related financial risk is borne by the fund manager. For the DC pension, the contribution rate is determined in advance, and the amount of the contribution depends on the investment rate of the pension. The related financial risks are borne by the insured. As the population evolves and the capital market develops, the DC old-age pension plays an increasingly important role in the social security system. Future retirement benefits cannot be guaranteed, so the DC pension scheme with minimum income protection has attracted many researchers' attention, and under the condition that the interest rate and volatility of asset investment are both random, It is necessary to discuss the optimal investment strategy. According to the current situation of the financial market, investors can invest their money in cash. In this paper, we study the investment problem of DC pension with minimum income guarantee under stochastic interest rate and stochastic volatility model. In the first chapter, we introduce the financial market and the most important of DC pension. The second chapter is the preparatory knowledge of this paper. The third chapter introduces the financial market and introduces the problem of minimum return guarantee. Firstly, the explicit solution of optimal investment strategy under exponential utility function is obtained by dynamic programming principle. Secondly, the explicit expression of optimal investment strategy under logarithmic utility is obtained by using Legendre transform and duality theory. Numerical examples are given to analyze the influence of market parameters on the optimal investment strategy under exponential utility and logarithmic utility respectively. Chapter 4th gives the conclusions and prospects of the paper, the shortcomings and the future research directions.
【学位授予单位】：天津工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F842.67

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