基于4/2随机波动率模型考虑错误定价和保费退还条款的DC型养老金计划的均衡投资策略

Abstract

Abstract:

In this paper, we consider a time-consistent investment strategy for DC pension plan with a return of premiums clause and mispricing under the mean-variance criterion. We assume that the pension plan manager is allowed to invest the wealth in the pension account in a financial market consisting of a risk-free asset, a pair of mispriced stocks, and a market index following a $4/2$ stochastic volatility model. Under the framework of game theory, the explicit expressions of the time-consistent equilibrium investment strategy and the equilibrium efficient frontier are obtained by using stochastic control methods and solving the extended HJB system. Finally, the effects of risk aversion coefficient, mispricing and return of premiums clauses on equilibrium strategy and efficient frontier are illustrated by numerical simulations.

Key words: Defined contribution pension plan, Mean-variance criterion, $4/2$ stochastic volatility model, Return of premiums clauses, Mispricing, Equilibrium strategy

CLC Number:

O211.67

Lu Jiaxin,Dong Hua. Equilibrium Investment Strategy of DC Pension Plan with Mispricing and Return of Premiums Clauses Under the 4/2 Stochastic Volatility Model[J].Acta mathematica scientia,Series A, 2023, 43(3): 939-956.

Trendmd

Figures/Tables 7

References 27

[1]	Bian L, Li Z, Yao H. Pre-commitment and equilibrium investment strategies for the DC pension plan with regime switching and a return of premiums clause. Insurance: Mathematics and Economics, 2018, 81: 78-94 doi: 10.1016/j.insmatheco.2018.05.005
[2]	Björk T, Murgoci A. A general theory of Markovian time inconsistent stochastic control problems. Ssrn Electronic Journal, 2010, 18(3): 545-592
[3]	Chang H, Li J. Robust equilibrium strategy for DC pension plan with the return of premiums clauses in a jump-diffusion model. Optimization, 2021: 1-30
[4]	Cheng Y, Escobar-Anel M. Optimal investment strategy in the family of $4/2$ stochastic volatility models. Quantitative Finance, 2021, 21: 1-29 doi: 10.1080/14697688.2020.1825781
[5]	Grasselli M. The $4/2$ stochastic volatility model: A unified approach for the Heston and the $3/2$ model. Mathematical Finance, 2017, 27(4): 1013-1034 doi: 10.1111/mafi.2017.27.issue-4
[6]	Gu A, Viens F G, Yao H. Optimal robust reinsurance-investment strategies for insurers with mean reversion and mispricing. Insurance: Mathematics and Economics, 2018, 80: 93-109 doi: 10.1016/j.insmatheco.2018.03.004
[7]	Gu A, Viens F G, Yi B. Optimal reinsurance and investment strategies for insurers with mispricing and model ambiguity. Insurance: Mathematics and Economics, 2017, 72: 235-249 doi: 10.1016/j.insmatheco.2016.11.007
[8]	Guan G, Liang Z. Optimal management of DC pension plan in a stochastic interest rate and stochastic volatility framework. Insurance: Mathematics and Economics, 2014, 57: 58-66 doi: 10.1016/j.insmatheco.2014.05.004
[9]	Guan G, Liang Z. Mean-variance efficiency of DC pension plan under stochastic interest rate and mean-reverting returns. Insurance: Mathematics and Economics, 2015, 61: 99-109 doi: 10.1016/j.insmatheco.2014.12.006
[10]	He L, Liang Z X. Optimal investment strategy for the DC plan with the return of premiums clauses in a mean-variance framework. Insurance: Mathematics and Economics, 2013, 53(3): 643-649 doi: 10.1016/j.insmatheco.2013.09.002
[11]	Heston S L. A closed-form solution for options with stochastic volatility with applications to bond and currency options. The Review of Financial Studies, 1993, 6(2): 327-343 doi: 10.1093/rfs/6.2.327
[12]	Heston S L. A simple new formula for options with stochastic volatility. Social Science Electronic Publishing, 1997, 15(4): 23-44
[13]	Kohler P H, Kohler I. Frailty modeling for adult and old age mortality: the application of a modified De Moivre Hazard function to sex differentials in mortality. Demographic Research, 2000, 3(8): 1-32
[14]	Li D, Ng W L. Optimal dynamic portfolio selection: Multi-period mean-variance formulation. Mathematical Finance, 2000, 10(3): 387-406 doi: 10.1111/mafi.2000.10.issue-3
[15]	Li D P, Rong X M, Zhao H, Yi B. Equilibrium investment strategy for DC pension plan with default risk and return of premiums clauses under CEV model. Insurance: Mathematics and Economics, 2017, 72: 6-20 doi: 10.1016/j.insmatheco.2016.10.007
[16]	Liu J, Timmermann A. Optimal convergence trade strategies. The Review of Financial Studies, 2013, 26: 1048-1086 doi: 10.1093/rfs/hhs130
[17]	Liu Z L, Wang Y J, Huang Y, Zhou J M. Optimal portfolios for the DC pension fund with mispricing under the HARA utility framework. Journal of Industrial and Management Optimization, 2023, 19(2): 1262-1281 doi: 10.3934/jimo.2021228
[18]	Ma J, Zhao H, Rong X. Optimal investment strategy for a DC pension plan with mispricing under the Heston model. Communications in Statistics-Theory and Methods, 2020, 49(13): 3168-3183 doi: 10.1080/03610926.2019.1586938
[19]	Markowit H. Portfolio selection. The Journal of Finance, 1952, 7(1): 77-91
[20]	Mudzimbabwe W. A simple numerical solution for an optimal investment strategy for a DC pension plan in a jump diffusion model. Journal of Computational and Applied Mathematics, 2019, 360: 55-61 doi: 10.1016/j.cam.2019.03.043
[21]	Wang Y J, Deng Y C, Huang Y, Zhou J M. Optimal reinsurance-investment policies for insurers with mispricing under mean-variance criterion. Communications in Statistics-Theory and Methods, 2020, 49: 1-28 doi: 10.1080/03610926.2018.1532006
[22]	Wang W Y, Muravey D, Shen Y, Zeng Y. Optimal investment and reinsurance strategies under $4/2$ stochastic volatility model. Scandinavian Actuarial Journal, 2022: 1-37
[23]	Wang P Q, Rong X M, Zhao H, Wang Y J. Robust optimal insurance and investment strategies for the government and the insurance company under mispricing phenomenon. Communications in Statistics-Theory and Methods, 2021, 50: 993-1017 doi: 10.1080/03610926.2019.1646765
[24]	Wang P, Shen Y, Zhang L, Kang Y X. Equilibrium investment strategy for a DC pension plan with learning about stock return predictability. Insurance: Mathematics and Economics, 2021, 100: 384-407 doi: 10.1016/j.insmatheco.2021.07.001
[25]	Yao H X, Lai Y Z, Ma Q H, Jian M J. Asset allocation for a DC pension fund with stochastic income and mortality risk: a multi-period mean-variance framework. Insurance: Mathematics and Economics, 2014, 54(1): 84-92 doi: 10.1016/j.insmatheco.2013.10.016
[26]	Zhang Y. Dynamic optimal mean-variance investment with mispricing in the family of $4/2$ stochastic volatility models. Mathematics, 2021, 9(18): 2293 doi: 10.3390/math9182293
[27]	Zhou X Y, Li D. Continuous-time mean-variance portfolio selection: A stochastic LQ framework. Applied Mathematics and Optimization, 2000, 42(1): 19-33 doi: 10.1007/s002450010003

Equilibrium Investment Strategy of DC Pension Plan with Mispricing and Return of Premiums Clauses Under the 4/2 Stochastic Volatility Model

RichHTML

PDF (PC)

Abstract

Cite this article

share this article

Figures/Tables 7

References 27

Related Articles 1

Metrics

Comments

Recommended 10