基于确定缴费型养老金最优投资的随机微分博弈

Stochastic Differential Games for Defined Contribution Pension with Optimal Investment

研究2种情况下养老金的随机微分博弈:第一种情况是基于效用的随机微分博弈,第二种情况是基于均值-方差准则的随机微分博弈.对于第一种情况在指数效用和幂效用下,应用线性-二次控制理论得到最优投资、市场策略和值函数的显示解.对于第二种情况,通过把原先的基于均值-方差准则的随机微分博弈转化为无限制情况,应用线性-二次控制理论得到无限制情况下最优投资、市场策略和有效边界的显示解;进而得到原基于均值-方差准则的随机微分博弈的最优投资、市场策略和有效边界的显示解.通过研究,可以指导养老金计划者在金融市场出现最坏时进行合理投资使自身的财富最大化;也可以指导养老金计划者在金融市场出现最坏时进行合理投资,使自身获得一定的财富,而面临的风险最小.

This paper researches two cases stochastic differential game for pension： the first is stochastic differential game based on the utility,the second case is stochastic differential game based on the mean-variance criteria. In the first case under the exponential utility and power utility,by applying linear-guadratic control theory,the explicit expressions of optimal investment strategies and optimal market strategies as well as of the value function are obtained. For the second case,by changing the original stochastic differential game based on the mean-variance criteria into unrestricted cases,applying linear-quadratic control theory,the explicit expressions of optimal investment strategies and optimal market strategies as well as of efficient frontier are obtained; finally get optimal investment strategies and optimal market strategies as well as of efficient frontier for the original stochastic differential game. When the market is worst,this research could be used to guide investor of pension to select the appropriate investment strategy for maximization his wealth and minimum the risk.