中文

Operations Research Transactions >

2025 , Vol. 29 >Issue 1: 127 - 141

DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2025.01.011

Robust optimal investment and benefit payment adjustment strategy for target benefit pension plans with stochastic salary

Expand
  • 1. School of Science, Hebei University of Technology, Tianjin 300401, China

Received date: 2021-07-21

  Online published: 2025-03-08

Copyright

, 2025, All rights reserved. Unauthorized reproduction is prohibited.
Fold

Abstract

This paper considers the optimal investment and benefit payment problem with default risk and model uncertainty under target benefit plans~(TBPs). The pension funds can be invested in a risk-free asset, a stock whose price process follows Heston model and a defaultable bond. In particular, the salary of TBPs members is stochastic. Using the stochastic optimal control approach, we derive the robust optimal strategies as well as the corresponding value functions in the post-default and pre-default, respectively. Besides, we also consider the optimal strategies for the non-ambiguity case. Finally, numerical analysis is provided to illustrate the effects of parameters on the optimal strategies, which provides an effective decision-making basis for pension managers.

Key words： target benefit pension plans; stochastic salary; ambiguity aversion; default risk; Hamilton-Jacobi-Bellman equation

Cite this article

Xinru ZHANG, Shixia MA, Yumeng ZHANG, Rui MU . Robust optimal investment and benefit payment adjustment strategy for target benefit pension plans with stochastic salary[J]. Operations Research Transactions, 2025 , 29(1) : 127 -141 . DOI: 10.15960/j.cnki.issn.1007-6093.2025.01.011

References

1 Qian L Y , Shen Y , Wang W , et al. Valuation of risk-based premium of DB pension plan with terminations[J]. Insurance: Mathematics and Economics, 2019, 86, 51- 63.
2 Chen Z , Li Z F , Zeng Y , et al. Asset allocation under loss aversion and minimum performance constraint in a DC pension plan with inflation risk[J]. Insurance: Mathematics and Economics, 2017, 75, 137- 150.
3 Bian L H , Li Z F , Yao H X . Pre-commitment and equilibrium investment strategies for the DC pension plan with regime switching and a return of premiums clause[J]. Insurance: Mathematics and Economics, 2018, 81, 78- 94.
4 Westerhout E. Intergenerational risk sharing in time-consistent funded pension schemes [EB/OL]. (2011-03-01)[2021-06-28]. https://api.semanticscholar.org/CorpusID:62812089.
5 Bommel J V. Intergenerational risk sharing and bank raids [EB/OL]. (2007-12-01)[2021-06-28]. http://dx.doi.org/10.2139/ssrn.965178.
6 Wang S X , Lu Y , Sanders B . Optimal investment strategies and intergenerational risk sharing for target benefit pension plans[J]. Insurance: Mathematics and Economics, 2018, 80, 1- 14.
7 Wang S X , Rong X M , Zhao H . Optimal investment and benefit payment strategy under loss aversion for target benefit pension plans[J]. Applied Mathematics and Computation, 2019, 346, 205- 218.
8 Wang S X , Lu Y . Optimal investment strategies and risk-sharing arrangements for a hybrid pension plan[J]. Insurance: Mathematics and Economics, 2019, 89, 46- 62.
9 Zhu H N , Cao M , Zhang C K . Time-consistent investment and reinsurance strategies for meanvariance insurers with relative performance concerns under the Heston model[J]. Finance Research Letters, 2019, 30, 280- 291.
10 A C X , Li Z F . Optimal investment and excess-of-loss reinsurance problem with delay for an insurer under Heston's SV model[J]. Insurance: Mathematics and Economics, 2015, 61, 181- 196.
11 Zhang Y , Zhao P B , Kou B Y . Optimal excess-of-loss reinsurance and investment problem with thinning dependent risks under Heston model[J]. Journal of Computation and Applied Mathematics, 2021, 382, 113082.
12 Wang P , Li Z F . Robust optimal investment strategy for an AAM of DC pension plans with stochastic interest rate and stochastic volatility[J]. Insurance: Mathematics and Economics, 2018, 80, 67- 83.
13 Wang N , Zhang N , Jin Z , et al. Robust non-zero-sum investment and reinsurance game with default risk[J]. Insurance: Mathematics and Economics, 2019, 84, 115- 132.
14 Wang N , Zhang N , Jin Z , et al. Reinsurance-investment game between two mean-variance insurers under model uncertainty[J]. Journal of Computation and Applied Mathematics, 2021, 382, 113095.
15 Sun Z Y , Zheng X X , Zhang X . Robust optimal investment and reinsurance of an insurer under variance premium principle and default risk[J]. Journal of Mathematical Analysis and Applications, 2017, 446, 1666- 1686.
16 Wang S X , Rong X M , Zhao H . Optimal time-consistent reinsurance-investment strategy with delay for an insurer under a defaultable market[J]. Journal of Mathematical Analysis and Applications, 2019, 474, 1267- 1288.
17 Zhu J Q , Guan G H , Li S H . Time-consistent non-zero-sum stochastic differential reinsurance and investment game under default and volatility risks[J]. Journal of Computational and Applied Mathematics, 2020, 374, 112737.
18 Wang P Q , Rong X M , Zhao H , et al. Robust optimal investment and benefit payment adjustment strategy for target benefit pension plans under default risk[J]. Journal of Computational and Applied Mathematics, 2021, 391, 113382.
19 张初兵, 荣喜民, 常浩. CEV模型下有随机工资DC型养老金的最优投资[J]. 工程数学学报, 2013, 30 (1): 1- 9.
20 Zeng Y , Li D P , Chen Z , et al. Ambiguity aversion and optimal derivative-based pension investment with stochastic income and volatility[J]. Journal of Economic Dynamics & Control, 2018, 88, 70- 103.
21 Maenhout P . Robust portfolio rules and asset pricing[J]. Review of Financial Studies, 2004, 17, 951- 983.
Options
Outlines

/

〈 〉