一类随机模型下DC养老金的最优投资策略

Optimal investment strategy under a stochastic model for DC pension

研究了DC型养老金计划参与者的最优投资策略,其中金融市场由一个无风险资产和一个风险资产组成,风险的市场价格由仿射平方根随机模型描述。利用随机控制理论,通过求解相应的Hamiltion-Jacobi-Bellman(HJB)方程,得到CRRA效用下最优值函数和最优投资策略的解析式。最后,通过数值算例,阐述了风险资产的随机因子和漂移率对最优投资策略的影响,并发现当市场往良性状态发展时,投资在风险资产的财富比例将不断增大;但在相同的市场状态下,当初始财富足够大时,投资在风险资产的财富比例几乎与投资期限无关。

The optimal investment strategy of the participants in the DC pension plan is studied.The financial market consists of a risk-free asset and a risky asset,and the market price of risk depends on affine-form square-root stochastic model.By using the stochastic control theory and solving the corresponding Hamiltion-Jacobi-Bellman(HJB)equation,the analytic expressions of the optimal value function and the optimal investment strategy under the CRRA utility are obtained.Finally,through numerical examples,the impact of stochastic factor and appreciation rate of the risky asset on the optimal investment strategy are explained,and it is found that the wealth proportion invested in the risky asset will continue to increase when the market state is developing to a positive state;but in the same market state,the optimal investment proportion is almost not affected by the investment period when the initial wealth is large enough.