Heston模型下DC型养老金鲁棒最优投资问题

Optimal Investment Strategy for a Robust DC Pension Plan under the Heston Model

本文研究在随机工资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.在模型中,养老金账户中的资本可以投资于一种风险资产和一种无风险资产,假设风险资产价格满足Heston模型.研究目标是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,我们求出了在幂效用函数和指数效用函数下鲁棒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.

We consider an optimal robust investment problem for a defined contribution DC pension plan with stochastic income and model uncertainty.In the model,the pension account is allowed to invest into a risky asset and a risk-free asset,and the dynamic of the price of risky asset follows a Heston model.The objective of the problem is to maximize the expected utility of the terminal relative wealth by choosing admissible investment strategies.By using the stochastic control dynamic programming approach,we find the robust optimal investment strategy and the corresponding value function when the utility function has the power or the exponential form,respectively.At last,we show a numerical example to further analyze the theoretical results through the MATLAB software.