Optimal Asset Allocation with Inflation Risk and Heston’s Stochastic Volatility

doi:10.12005/orms.2017.0020

Operations Research and Management Science ›› 2017, Vol. 26 ›› Issue (1): 148-155.DOI: 10.12005/orms.2017.0020

• Application Research • Previous Articles Next Articles

Optimal Asset Allocation with Inflation Risk and Heston’s Stochastic Volatility

SUN Jing-yun¹, ZHENG Jun², ZHANG Ling³

1.School of Mathematics, Lanzhou City University, Lanzhou 730070, China;
2.School of Finance, Guangdong University of Finance &
Economics, Guangzhou 510275, China;
3.Department of Economic and Trade, Guangdong University of Finance, Guangzhou 510521, China

Received:2015-03-15 Online:2017-01-20

基于通货膨胀风险和Heston随机波动率下的最优资产配置

孙景云¹, 郑军², 张玲³

1.兰州城市学院数学学院,甘肃兰州730070;
2.广东财经大学金融学院,广东广州510275;
3.广东金融学院经济贸易系,广东广州510521

作者简介:孙景云(1982-),男,甘肃临潭人,博士,讲师,研究方向:金融数学与金融工程;郑军(1981-),男,贵州松桃人,博士,研究方向:金融市场与投资;张玲(1979-),女,山东临沂人,博士,副教授,研究方向:金融工程与风险管理。
基金资助:
甘肃省城市发展研究院资助项目(2014-GSCFY-KJ02);教育部人文社会科学基金资助项目(13YJCZH247);广东省哲学社会科学基金资助项目(GD12XYJ06);甘肃省高等学校科研项目(2013A-097);兰州城市学院重点学科立项资助作者简介:孙景云(1982-),男,甘肃临潭人,博士,讲师,研究方向:金融数学与金融工程;郑军(1981-),男,贵州松桃人,博士,研究方向:金融市场与投资;张玲(1979-),女,山东临沂人,博士,副教授,研究方向:金融工程与风险管理。基于通货膨胀风险和Heston随机波动率下的最优资产配置孙景云¹, 郑军², 张玲³(1.兰州城市学院数学学院,甘肃兰州730070;2.广东财经大学金融学院,广东广州510275;3.广东金融学院经济贸易系,广东广州510521)摘要:本文考虑了基于均值-方差准则下的连续时间投资组合选择问题。为了对冲市场中的利率风险和通货膨胀风险,假定市场上存在可供交易的零息名义债券和零息通货膨胀指数债券。另外,投资者还可以投资一个价格具有Heston随机波动率的风险资产。首先建立了基于均值-方差框架下的最优投资组合问题,然后将原问题进行转换,利用随机动态规划方法和对偶Lagrangian原理,获得了均值-方差准则下的有效投资策略以及有效前沿的解析表达形式,最后对相关参数的敏感性进行了分析。

Abstract

Abstract: In this paper,we consider the continuous time optimal investment portfolio problem under mean-variance criterion. In order to hedge the risks of interest and inflation in the market, we assume that the financial market consists of an nominal zero-coupon bond and an inflation-indexed bond,and a risky asset who’s price follows Heston’s stochastic volatility. We first establish an optimal investment portfolio problem under mean-variance criterion. Then we transform the original problem into a tractable one,and by using stochastic dynamic programming and dual Lagrangian theorem, a closed-form of the efficient policy and the efficient frontier are obtained. Finally, a sensibility analysis is provided for corresponding parameters.

Key words: mean-variance criterion, inflation-indexed bond, HJB equation, dual lagrangian theorem, efficient frontier

摘要： 本文考虑了基于均值-方差准则下的连续时间投资组合选择问题。为了对冲市场中的利率风险和通货膨胀风险,假定市场上存在可供交易的零息名义债券和零息通货膨胀指数债券。另外,投资者还可以投资一个价格具有Heston随机波动率的风险资产。首先建立了基于均值-方差框架下的最优投资组合问题,然后将原问题进行转换,利用随机动态规划方法和对偶Lagrangian原理,获得了均值-方差准则下的有效投资策略以及有效前沿的解析表达形式,最后对相关参数的敏感性进行了分析。

关键词: 均值-方差准则, 通胀指数债券, HJB方程, 对偶 Lagrangian 原理, 有效前沿

CLC Number:

F830.59
F224

SUN Jing-yun, ZHENG Jun, ZHANG Ling. Optimal Asset Allocation with Inflation Risk and Heston’s Stochastic Volatility[J]. Operations Research and Management Science, 2017, 26(1): 148-155.

孙景云, 郑军, 张玲. 基于通货膨胀风险和Heston随机波动率下的最优资产配置[J]. 运筹与管理, 2017, 26(1): 148-155.

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Optimal Asset Allocation with Inflation Risk and Heston’s Stochastic Volatility

基于通货膨胀风险和Heston随机波动率下的最优资产配置

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