基于模型不确定性有违约风险的混合养老金问题

摘要/Abstract

摘要：

该文在违约风险下研究了基于模型不确定性的连续时间集体混合型养老金计划的最优投资和最优缴款--给付调整策略. 假设养老基金允许投资于由无风险资产和价格服从 4/2 随机波动率模型的股票以及违约债券组成的金融市场. 该文的目标是在 CARA 效用函数基础上最大化盈余和缴款--给付调整额的贴现值或当盈余和缴款--给付调整额为负时将其贴现值最小化. 利用随机最优控制方法, 分别推导出违约前和违约后情况下的鲁棒最优策略和相应值函数. 最后通过数值分析展示了模型参数和金融市场参数对最优策略的影响.

关键词: 混合型养老金, 4/2 随机波动率模型, 违约风险, 模型不确定性

Abstract:

This paper considers the optimal investment and optimal contribution-benefit adjustment strategies of a continuous time collective hybrid pension plan with model uncertainty and default risk. We assume that pension funds are invested in a risk-free asset, a defaultable bond and a stock satisfied 4/2 random volatility model. The objective is to maximize the discount value of surplus and contribution-benefit adjustment amount or minimize the discount value when surplus and contribution-benefit adjustment amount are negative based on the CARA utility function. Firstly, applying stochastic optimal control approach, we establish the Hamilton-Jacobi-Bellman equations for both the pre-default case and the post-default case, respectively. Then, we derive the closed-from solutions for robust optimal strategies and corresponding value functions. Finally, numerical analyses illustrate the influence of model parameters and financial market parameters on optimal control problems.

Key words: hybrid pension, 4/2 stochastic volatility model, default risk, model uncertainty

中图分类号:

F224

姜福蕾, 董华. 基于模型不确定性有违约风险的混合养老金问题[J]. 数学物理学报, 2025, 45(4): 1354-1372.

Jiang Fulei, Dong Hua. On the Hybrid Pension with Model Uncertainty and Default Risk[J]. Acta mathematica scientia,Series A, 2025, 45(4): 1354-1372.

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