Heston模型下具有违约风险的DC型养老金计划的均衡投资策略

Equilibrium Investment Strategy of DC Pension Plan with Default Risk Under Heston Model

将资产投资于无风险资产、风险资产和违约债券,在MV标准下得出DC型养老金的均衡投资策略,风险资产价格服从Heston模型。在现实中,存在缴费人提前死亡,以及在积累阶段,一部分养老金成员可能会死亡的情况,他们的保险费应被撤回,其余的尚存成员则平均分配收益和积累之间的差额。所以考虑将缴费的一部分投入到违约债券从而保护缴款人的利益。在均值方差的原则前提下,利用动态规划原理,建立了相应的HJB(Hamilton Jacob Bellman)方程并求解,得出最优的资产分配策略使得最后的收益达到最大并且损失最小。最后使用Matlab软件进行数值模拟,分析各项参数对DC型养老金最优策略的影响。

Assets are invested in risk-free assets,risky assets and default bonds,and the equilibrium investment strategy of DC pension is obtained under MV standard.The risk asset price obeys the Heston model.In reality,there also exist early deaths of contributory members.In the accumulation phase,some pension members may die,and their insurance premiums should be withdrawn,while the rest of the surviving members divide the difference between the benefits and the accumulation equally.So the paper suggests putting a portion of the contribution into the default bond to protect the benefit of the contributor.On the premise of the principle of mean variance,the corresponding HJB(Hamilton-Jacob-Bellman)equation is established and solved by using the principle of dynamic programming,and the optimal asset allocation strategy is obtained to maximize the final income and minimize the loss.Finally,Matlab software was used for numerical simulation to analyze the influence of various parameters on the DC pension optimal strategy.