Heston模型下考虑工资风险和保费退还条款的DC型养老金时间一致性投资策略

DC型养老金投资者通常可以将保费投资于金融市场中无风险资产、风险资产以及通胀指数化债券3种资产。在均值-方差准则下，为了充分考虑市场风险因素和保障参保人利益，将通胀风险、波动风险、工资风险以及保费退还条款引进投资模型中。利用博弈论思想和随机最优控制技术，通过求解一个扩展HJB方程组，得到了最优时间一致性投资策略和有效前沿的解析表达。最后，通过数值分析比较了有、无保费退还条款两种情形下的最优投资策略。此外，还分析了一些主要参数对最优投资策略和有效前沿的影响，并给出了经济意义上的解释。

Time-Consistent Investment Strategy for DC Pension with Salary Risk and Premium Refund Clauses in Heston Model

DC (defined contribution) pension investors can usually invest premiums in three assets in the financial market: risk-free assets, risky assets, and inflation-linked bonds. In this paper, under the mean-variance criterion, in order to fully consider the market risk factors and protect the interests of the insured, the inflation risk, volatility risk, salary risk, and premium refund clause are introduced into the investment model. Besides, by using the game theory and the stochastic optimal control technique, the explicit solutions to the optimal time-consistent investment strategy and the efficient frontier are obtained by solving an extended HJB equation. Moreover, the optimal investment strategy in the two cases with and without the premium refund clause is compared by numerical analysis. Furthermore, the effect of some main parameters on the optimal investment strategy and efficient frontier is analyzed, and economic interpretations are given.