基于损失厌恶和LEL约束下的DC养老金计划的最优投资  

Optimal Investment of DC Pension Plan Under Loss Aversion and LEL Constraint

作　　者：董迎辉 魏思媛 吕文欣 殷子涵 DONG Yinghui;WEI Siyuan;LV Wenxin;YIN Zihan(Department of Mathematics,Suzhou University of Science and Technology,Suzhou 215009,China)

机构地区：[1]苏州科技大学数科院,苏州215009

出　　处：《应用数学学报》2023年第2期291-312,共22页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(12071335);教育部人文社科基金(20YJAZH025);江苏省第六期333高层次人才培养工程资助项目。

摘　　要：研究了DC型养老金经理在损失厌恶和有限期望损失约束下的最优投资组合问题.利用凹化方法得到了基于有限期望损失约束下的DC型养老金的最优财富过程的解析表达式,并进一步比较了在前景理论框架下有限期望损失约束和VaR约束对最优投资行为的影响.虽然在凹效用最大化问题中,当经济非常萧条时,有限期望损失约束下所发生的损失要低于VaR约束下所发生的损失,从而使得有限期望损失约束被认为是一个比VaR约束更有效的风险管理方法,但是在本文所考虑的非凹效用最大化问题中,理论与数值结果表明,当保护水平不是太高时,DC型养老金的最优财富在有限期望损失约束下具有与VaR约束下相同形式的表达公式,也就是说,有限期望损失约束与VaR约束存在着等价关系.因此,在非凹效用框架下,基于有限期望损失约束的风险管理并不比基于VaR约束的风险管理更具有优势,对于损失厌恶型的投资者,需要设计其它有效的风险管理方法来更好地改进对DC型养老金计划的风险管理.We investigate the optimal investment problem of a DC pension fund manager under loss aversion and a limited expectation losses(LEL)constraint.We apply the concavification technique to solve the LEL-constrained problem and derive the closedform representations of the optimal wealth and portfolio processes.Furthermore,we compare the effects of a VaR and a LEL constraint on the optimal investment behavior under prospect theory.Although a LEL constraint can provide a better protection for the investors’benefits than a VaR constraint in a concave optimization problem since the VaR-based risk management will incur heavier losses than the LEL-based risk management in the worst financial states under a concave utility,in our non-concave optimization problem,theoretical and numerical results show that for a relatively low protection level,a VaR and a LEL constraint induce the same optimal terminal wealth and the same investment behavior,that is to say,there is an equivalence between a LEL and a VaR constraint.Therefore,under a non-concave utility,the LEL-based risk management has lost its advantage over the VaR-based risk management.It needs to design a more efficient risk measure for loss averse investors to improve the risk management for a DC pension plan.

关 键 词：有限期望损失约束 DC型养老金计划 损失厌恶 凹化 

分 类 号：F832.48[经济管理—金融学]