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Equilibrium investment strategy for DC pension plan with default risk and return of premiums clauses under CEV model

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  • Li, Danping
  • Rong, Ximin
  • Zhao, Hui
  • Yi, Bo

Abstract

This paper considers an optimal investment problem for a defined contribution (DC) pension plan with default risk in a mean–variance framework. In the DC plan, contributions are supposed to be a predetermined amount of money as premiums and the pension funds are allowed to be invested in a financial market which consists of a risk-free asset, a defaultable bond and a risky asset satisfied a constant elasticity of variance (CEV) model. Notice that a part of pension members could die during the accumulation phase, and their premiums should be withdrawn. Thus, we consider the return of premiums clauses by an actuarial method and assume that the surviving members will share the difference between the return and the accumulation equally. Taking account of the pension fund size and the volatility of the accumulation, a mean–variance criterion as the investment objective for the DC plan can be formulated, and the original optimization problem can be decomposed into two sub-problems: a post-default case and a pre-default case. By applying a game theoretic framework, the equilibrium investment strategies and the corresponding equilibrium value functions can be obtained explicitly. Economic interpretations are given in the numerical simulation, which is presented to illustrate our results.

Suggested Citation

  • Li, Danping & Rong, Ximin & Zhao, Hui & Yi, Bo, 2017. "Equilibrium investment strategy for DC pension plan with default risk and return of premiums clauses under CEV model," Insurance: Mathematics and Economics, Elsevier, vol. 72(C), pages 6-20.
    • Handle: RePEc:eee:insuma:v:72:y:2017:i:c:p:6-20
    DOI: 10.1016/j.insmatheco.2016.10.007
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    References listed on IDEAS

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    Cited by:

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    2. Yanfei Bai & Zhongbao Zhou & Helu Xiao & Rui Gao & Feimin Zhong, 2021. "A stochastic Stackelberg differential reinsurance and investment game with delay in a defaultable market," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 94(3), pages 341-381, December.
    3. Liyuan Wang & Zhiping Chen, 2019. "Stochastic Game Theoretic Formulation for a Multi-Period DC Pension Plan with State-Dependent Risk Aversion," Mathematics, MDPI, vol. 7(1), pages 1-16, January.
    4. Bian, Lihua & Li, Zhongfei & Yao, Haixiang, 2018. "Pre-commitment and equilibrium investment strategies for the DC pension plan with regime switching and a return of premiums clause," Insurance: Mathematics and Economics, Elsevier, vol. 81(C), pages 78-94.
    5. Yang Wang & Xiao Xu & Jizhou Zhang, 2021. "Optimal Investment Strategy for DC Pension Plan with Stochastic Income and Inflation Risk under the Ornstein–Uhlenbeck Model," Mathematics, MDPI, vol. 9(15), pages 1-15, July.
    6. Frank Bosserhoff & An Chen & Nils Sorensen & Mitja Stadje, 2021. "On the Investment Strategies in Occupational Pension Plans," Papers 2104.08956, arXiv.org.
    7. Zilan Liu & Yijun Wang & Ya Huang & Jieming Zhou, 2022. "Optimal Time-Consistent Investment and Premium Control Strategies for Insurers with Constraint under the Heston Model," Mathematics, MDPI, vol. 10(7), pages 1-22, March.
    8. Josa-Fombellida, Ricardo & López-Casado, Paula & Rincón-Zapatero, Juan Pablo, 2018. "Portfolio optimization in a defined benefit pension plan where the risky assets are processes with constant elasticity of variance," Insurance: Mathematics and Economics, Elsevier, vol. 82(C), pages 73-86.

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    More about this item

    Keywords

    DC pension plan; Default risk; Constant elasticity of variance (CEV) model; Mean–variance criterion; Time-consistency;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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