基于通货膨胀风险和Heston随机波动率下的最优资产配置

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

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。

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.