跳跃不确定过程下的养老金最优投资策略

Optimal Pension Investment Strategy Problem with Uncertain Jump Diffusion Process

在不确定理论的框架下,研究具有不确定工资的确定缴费(DC)型养老金的最优投资策略问题.在最优化模型中,假设风险资产的价格服从跳跃不确定过程,养老金在无风险资产和风险资产上进行投资,养老金控制的目标是选择最优给付率和投资策略,以使其二次损失函数现值最小化.利用不确定动态规划法,证明了不确定最优性原理,得出了不确定最优性方程,通过求解不确定最优性方程得到最优给付率和最优投资策略的显式解.

This paper studies the optimal investment strategy problem for a defined contribution pension fund（DC）with uncertain salary under the uncertain theory framework.The pension funds are allowed to invest in a risk-free asset and a risky asset whose price follows a jump diffusion process.We set up the optimal investment model to minimize the quadratic loss function.By applying the uncertain dynamic programming technique,we develop an optimality principle and obtain an optimality equation.Furthermore,by using optimality equation,we obtain the explicit form solutions of optimal investment strategy and optimal benefit rate.