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《山东大学学报(理学版)》 ›› 2025, Vol. 60 ›› Issue (3): 49-59.doi: 10.6040/j.issn.1671-9352.0.2023.436

• 金融数学 • 上一篇    下一篇

4/2模型下目标给付型养老金计划的最优投资和给付策略

韩婧怡,常浩*,陈祯   

  1. 天津工业大学数学科学学院, 天津 300387
  • 发布日期:2025-03-10
  • 通讯作者: 常浩(1979—),男,教授,博士生导师,博士,研究方向为数理金融与保险精算. E-mail:ch8683897@126.com
  • 作者简介:韩婧怡(2000— ),女,硕士研究生,研究方向为金融数学和保险精算. E-mail:1367769927@qq.com*通信作者:常浩(1979—),男,教授,博士生导师,博士,研究方向为数理金融与保险精算. E-mail:ch8683897@126.com
  • 基金资助:
    国家社会科学基金后期资助项目(21FJYB042)

Optimal investment and benefit payment adjustment strategy for target benefit pension plan under 4/2 stochastic volatility model

HAN Jingyi, CHANG Hao*, CHEN Zhen   

  1. School of Mathematical Sciences, Tiangong University, Tianjin 300387, China
  • Published:2025-03-10

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摘要： 4/2随机波动率下的目标给付型养老金(target benefit pension, TBP)计划包含在职成员和退休成员,在职成员向养老基金缴纳固定费用,退休成员从基金中领取相应养老金,退休成员的给付水平取决于基金的投资情况。假设养老金可以投资于一种无风险资产和一种股票,股票的价格过程遵循4/2随机波动率模型。运用随机最优控制理论,得到最优投资和给付调整策略的显式解,应用数值算例分析各模型参数对最优投资和给付调整策略的影响。该研究为随机波动率模型下的其他复杂投资问题的解决提供方法论基础,也为基金管理者的资产配置和风险管理提供参考依据。

关键词: 目标给付型养老金计划, 4/2随机波动率模型, 偏差型目标函数, 随机最优控制理论

Abstract: The target benefit pension(TBP)plan under 4/2 stochastic volatility model contains both the active members and the retired members, where the active members pay predetermined contributions to the pension fund and the retired members receive a corresponding pension from the fund, and the benefit payment level of the retired members depends on the investment situation. It is assumed that the pension fund can be invested in a risk-free asset and a stock, and the stock price follows the 4/2 stochastic volatility model. Applying the stochastic optimal control theory, explicit solutions for the optimal investment and benefit payment adjustment strategy are derived, and a numerical example is given to illustrate the results obtained. Methodological and theoretical support for solving other complex investment problems in a stochastic volatility environment, and the reference basis for asset allocation and risk management of fund managers are provided.

Key words: target benefit pension plan, 4/2 stochastic volatility model, deviation-type objective function, stochastic optimal control theory

中图分类号: 

  • O211.67
[1] HABERMAN S, SUNG J H. Dynamic approaches to pension funding[J]. Insurance: Mathematics and Economics, 1994, 15(2):151-162.
[2] NGWIRA B, GERRARD R. Stochastic pension fund control in the presence of Poisson jumps[J]. Insurance: Mathematics and Economics, 2007, 40(2):283-292.
[3] BATTOCCHIO P, MENONCIN F. Optimal pension management in a stochastic framework[J]. Insurance: Mathematics and Economics, 2004, 34(1):79-95.
[4] ZHANG Ling, LI Danping, LAI Yongzeng. Equilibrium investment strategy for a defined contribution pension plan under stochastic interest rate and stochastic volatility[J]. Journal of Computational and Applied Mathematics, 2020, 368:112536.
[5] GERRARD R, HABERMAN S, VIGNA E. Optimal investment choices post-retirement in a defined contribution pension scheme[J]. Insurance: Mathematics and Economics, 2004, 35(2):321-342.
[6] CHANG Hao, WANG Chunfeng, FANG Zhenming, et al. Defined contribution pension planning with a stochastic interest rate and mean-reverting returns under the hyperbolic absolute risk aversion preference[J]. IMA Journal of Management Mathema-tics, 2020, 31(2):167-189.
[7] CHANG Hao, LI Jiaao. Robust equilibrium strategy for DC pension plan with the return of premiums clauses in a jump-diffusion model[J]. Optimization, 2023, 72(2):463-492.
[8] CHEN Lv, LI Danping, WANG Yumin, et al. The optimal cyclical design for a target benefit pension plan[J]. Journal of Pension Economics and Finance, 2023, 22(3):284-303.
[9] WANG Suxin, LU Yi, SANDERS B. Optimal investment strategies and intergenerational risk sharing for target benefit pension plans[J]. Insurance: Mathematics and Economics, 2018, 80:1-14.
[10] WANG Suxin, LU Yi. Optimal investment strategies and risk-sharing arrangements for a hybrid pension plan[J]. Insurance: Mathematics and Economics, 2019, 89:46-62.
[11] GOLLIER C. Intergenerational risk-sharing and risk-taking of a pension fund[J]. Journal of Public Economics, 2008, 92(5/6):1463-1485.
[12] CUI Jiajia, JONG D F, PONDS E. Intergenerational risk sharing within funded pension schemes[J]. Journal of Pension Economics and Finance, 2011, 10(1):1-29.
[13] RONG Ximin, CHENG Tao, ZHAO Hui. Target benefit pension plan with longevity risk and intergenerational equity[J]. ASTIN Bulletin: The Journal of the IAA, 2023, 53(1):84-103.
[14] LIU Zilan, ZHANG Huanying, HE Lei. Optimal assets allocation and benefit adjustment strategy with longevity risk for target benefit pension plans[J]. Journal of Industrial and Management Optimization, 2023, 19(6):3931-3951.
[15] HESTON S L. A simple new formula for options with stochastic volatility[EB/OL].(1997-09-19)[2023-10-16]. https://api.semanticscholar.org/CorpusID:150914514.
[16] GRASSELLI M. The 4/2 stochastic volatility model: a unified approach for the Heston and the 3/2 model[J]. Mathematical Finance, 2017, 27(4):1013-1034.
[17] CHENG Y Y, ESCOBAR A M. Robust portfolio choice under the 4/2 stochastic volatility model[J]. IMA Journal of Management Mathematics, 2022, 34(1):221-256.
[18] CHENG Y Y, ESCOBAR A M. Optimal investment strategy in the family of 4/2 stochastic volatility models[J]. Quantitative Finance, 2021, 21(10):1723-1751.
[19] LIN Wei, LI Shenghong, LUO Xingguo, et al. Consistent pricing of VIX and equity derivatives with the 4/2 stochastic volatility plus jumps model[J]. Journal of Mathematical Analysis and Applications, 2017, 447(2):778-797.
[20] WANG W Y, MURAVEY D, SHEN Y, et al. Optimal investment and reinsurance strategies under 4/2 stochastic volatility model[J]. Scandinavian Actuarial Journal, 2023, 2023(5):413-449.
[21] ZHANG Yumo. Mean-variance asset-liability management under CIR interest rate and the family of 4/2 stochastic volatility models with derivative trading[J]. Journal of Industrial and Management Optimization, 2023, 19(6):4022-4063.
[22] HATA H, YASUDA K. Expected power utility maximization with delay for insurers under the 4/2 stochastic volatility model[J]. Mathematical Control and Related Fields, 2024, 14(1):16-50.
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