通货膨胀下相对财富的鲁棒优化问题
Robust Optimization of Relative Wealth under Inflation
摘要: 本文研究了在随机工资、通货膨胀和模型不确定性影响下确定缴费型养老金的鲁棒最优投资问题。一般来说，DC型养老金的投资期限较长，所以，在投资期限内我们考虑真实的财富过程。文中主要采用随机动态理论和鲁棒最优控制方法求得相对财富的最优投资策略。在模型中，养老金被允许投资于一种风险资产和一种无风险资产，风险资产价格满足Heston模型。通过选择最优投资策略，使得养老金账户的终端相对财富效用最大化。利用随机动态规划的方法，求出了在幂效用函数下相对财富的最优投资策略和相应的值函数。最后，通过MATLAB软件对理论结果进行了数值分析。
Abstract: This paper studies the robust optimal investment problem of contributory pension under the influence of random wage, inflation and model uncertainty. Generally speaking, the investment period of DC pension is long, so we consider the real wealth process during the investment period. In this paper, the stochastic dynamic theory and robust optimal control method are used to obtain the optimal investment strategy of relative wealth. In the model, pension is allowed to invest in a risk asset and a risk-free asset, and the price of risk asset satisfies Heston model. By selecting the optimal investment strategy, the terminal relative wealth utility of pension account is maximized. Using the method of stochastic dynamic programming, the robust optimal investment strategy of relative wealth and the corresponding value function under the power utility function are obtained. Finally, the theoretical results are numerically analyzed by MATLAB software.
文章引用：郭云瑞. 通货膨胀下相对财富的鲁棒优化问题[J]. 理论数学, 2022, 12(5): 703-713. https://doi.org/10.12677/PM.2022.125081

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