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Portfolio optimization in a defined benefit pension plan where the risky assets are processes with constant elasticity of variance

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  • Josa-Fombellida, Ricardo
  • López-Casado, Paula
  • Rincón-Zapatero, Juan Pablo

Abstract

The paper studies the optimal asset allocation problem of a defined benefit pension plan that operates in a financial market composed of risky assets whose prices are constant elasticity variance processes. The benefits paid to the participants are deterministic. The contributions to the fund are designed by a spread amortization method, which takes into account the size of the unfunded actuarial liability, defined as the difference between the actuarial liability and the fund assets. We address the case where the fund manager wishes to minimize the solvency risk at the final date of the plan when the fund is underfunded, as well as the case where the fund manager wishes to maximize an increasing, constant elasticity utility function of the fund surplus, when the fund is overfunded. The optimal portfolio and contributions are obtained in both scenarios, with the help of the Hamilton–Jacobi–Bellman equation. A numerical illustration shows the evolution of the plan for several values of the elasticity parameter of the CEV price processes and the risk aversion of the manager, yielding some tips on the main properties of the optimal portfolio.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:insuma:v:82:y:2018:i:c:p:73-86
    DOI: 10.1016/j.insmatheco.2018.06.011
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    Cited by:

    1. Josa-Fombellida, Ricardo & Navas, Jorge, 2020. "Time consistent pension funding in a defined benefit pension plan with non-constant discounting," Insurance: Mathematics and Economics, Elsevier, vol. 94(C), pages 142-153.
    2. Guan, Guohui & Hu, Jiaqi & Liang, Zongxia, 2022. "Robust equilibrium strategies in a defined benefit pension plan game," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 193-217.
    3. Guohui Guan & Zongxia Liang & Yi Xia, 2023. "Optimal management of DB pension fund under both underfunded and overfunded cases," Papers 2302.08731, arXiv.org.
    4. Artem Dyachenko & Patrick Ley & Marc Oliver Rieger & Alexander F. Wagner, 2022. "The asset allocation of defined benefit pension plans: the role of sponsor contributions," Journal of Asset Management, Palgrave Macmillan, vol. 23(5), pages 376-389, September.
    5. Guohui Guan & Jiaqi Hu & Zongxia Liang, 2021. "Robust equilibrium strategies in a defined benefit pension plan game," Papers 2103.09121, arXiv.org.

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    More about this item

    Keywords

    Pension funding; Dynamic programming; CEV process; Risk management; Optimal portfolio;
    All these keywords.

    JEL classification:

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

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