违约风险下目标收益型养老金计划的α-鲁棒最优投资策略

摘要/Abstract

摘要：

该文研究具有违约风险和模型不确定性的目标收益养老金计划的最优投资和收益支付问题.假定养老基金投资于无风险资产、可违约债券和股票，其中股票价格服从常弹性方差（CEV）模型.养老金的支付取决于计划的财务状况，且风险由不同代人分担.同时为保障退休之前发生死亡的养老金持有者权益，在模型中加入保费返还条款.此外，该文的模型允许养老金管理者有不同程度的模糊厌恶，而不是只考虑极端的模糊厌恶.应用随机控制方法，分别建立违约后和违约前两种情况下的Hamilton-Jacobi-Bellman方程，推导出α-鲁棒的最优投资策略和最优福利调整策略的闭型解.最后数值分析说明了金融市场参数对最优控制问题的影响.

关键词: 目标收益计划, α-鲁棒, 代际风险分担, 违约风险, 保费返还

Abstract:

This paper considers the optimal investment and benefit payment problem for target benefit pension plan with default risk and model uncertainty. We assume that pension funds are invested in a risk-free asset, a defaultable bond and a stock satisfied a constant elasticity of variance(CEV) model. The payment of pensions depends on the financial status of the plan, with risk sharing between different generations. At the same time, in order to protect the rights of pension holders who dies before retirement, the return of premiums clauses is added to the model. In addition, our model allows the pension manager to have different levels of ambiguity aversion, instead of only considering extremely ambiguity-averse attitude. Using the stochastic optimal control approach, we establish the Hamilton-Jacobi-Bellman equations for both the post-default case and the pre-default case, respectively. We derive the closed-form solutions for α-robust optimal investment strategies and optimal benefit payment adjustment strategies. Finally, numerical analyses illustrate the influence of financial market parameters on optimal control problems.

Key words: Target benefit plan, α-robust, Intergenerational risk sharing, Default risk, Return of premiums

中图分类号:

O211.6

石媛,赵永霞. 违约风险下目标收益型养老金计划的α-鲁棒最优投资策略[J]. 数学物理学报, 2022, 42(3): 943-960.

Yuan Shi,Yongxia Zhao. α-Robust Optimal Investment Strategy for Target Benefit Pension Plans Under Default Risk[J]. Acta mathematica scientia,Series A, 2022, 42(3): 943-960.

图/表 9

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参考文献 22

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