WU Jin-jin,WANG Chuan-yu, ZHANG Jing.Robust Optimal Investment Strategy of DC Pension under Stochastic Interest Rate and Inflation[J].Journal of Chongqing Technology and Business University(Natural Science Edition）,2020,37(1):95-103

Robust Optimal Investment Strategy of DC Pension under Stochastic Interest Rate and Inflation

DOI：

 作者 单位 吴津津,王传玉,张静 安徽工程大学 数理学院，安徽 芜湖，241000

针对通货膨胀、随机利率、随机薪酬和模型不确定性影响下的确定缴费(Defined Contribution，DC)型养老金的鲁棒最优投资策略问题，首先假设市场是由无风险资产、滚动债券以及股票3种资产组成，给出这3种资产以及随机薪酬的动力学公式；然后通过消费者价格指数刻画通货膨胀的水平，应用伊藤公式，得到通货膨胀环境下3种资产价格以及随机薪酬的动力学公式；接着应用Girsanov定理，得到新测度下随机利率、3种资产以及随机薪酬的动力学公式，并得到养老金账户的财富过程；最后在期望效用最大化的原理下，应用随机控制理论求解HJB方程(Hamilton Jacobi Bellman equation),得到了DC养老金的鲁棒最优投资策略；通过数值分析得出通货膨胀对鲁棒最优投资策略的影响。

For the robust optimal investment strategy of Defined Contribution (DC) pension under the influence of inflation, stochastic interest rate, stochastic salary and model uncertainty; firstly, it is assumed that the market consists of three kinds of assets: risk-free assets, rolling bonds and stocks, and the dynamic formulas of these three kinds of assets and stochastic compensation are given. Then the level of inflation is depicted by the consumer price index, and Ito formula is applied to obtain the dynamic formulas of three asset prices and stochastic compensation under the inflation environment. Secondly, by applying Girsanov theorem, the dynamic formulas of stochastic interest rate, three kinds of assets and stochastic compensation under the new measure are obtained, and the wealth process of pension account is obtained. Finally, based on the principle of maximizing expected utility, the robust optimal investment strategy for DC pension is obtained by solving the HJB equation (Hamilton-Jacobi-Bellman equation) using stochastic control theory. The influence of inflation on robust optimal investment strategy is obtained through numerical analysis.