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Mean–variance target-based optimisation for defined contribution pension schemes in a stochastic framework

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  • Menoncin, Francesco
  • Vigna, Elena

Abstract

We solve a mean–variance optimisation problem in the accumulation phase of a defined contribution pension scheme. In a general multi-asset financial market with stochastic investment opportunities and stochastic contributions, we provide the general forms for the efficient frontier, the optimal investment strategy, and the ruin probability. We show that the mean–variance approach is equivalent to a “user-friendly” target-based optimisation problem which minimises a quadratic loss function, and provide implementation guidelines for the selection of the target. We show that the ruin probability can be kept under control through the choice of the target level. We find closed-form solutions for the special case of stochastic interest rate following the Vasiček (1977) dynamics, contributions following a geometric Brownian motion, and market consisting of cash, one bond and one stock. Numerical applications report the behaviour over time of optimal strategies and non-negative constrained strategies.

Suggested Citation

  • Menoncin, Francesco & Vigna, Elena, 2017. "Mean–variance target-based optimisation for defined contribution pension schemes in a stochastic framework," Insurance: Mathematics and Economics, Elsevier, vol. 76(C), pages 172-184.
    • Handle: RePEc:eee:insuma:v:76:y:2017:i:c:p:172-184
    DOI: 10.1016/j.insmatheco.2017.08.002
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    Cited by:

    1. Henrique Ferreira Morici & Elena Vigna, 2023. "Optimal additional voluntary contribution in DC pension schemes to manage inadequacy risk," Carlo Alberto Notebooks 699 JEL Classification: C, Collegio Carlo Alberto.
    2. Wang, Pei & Shen, Yang & Zhang, Ling & Kang, Yuxin, 2021. "Equilibrium investment strategy for a DC pension plan with learning about stock return predictability," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 384-407.
    3. Peter A. Forsyth, 2020. "A Stochastic Control Approach to Defined Contribution Plan Decumulation: "The Nastiest, Hardest Problem in Finance"," Papers 2008.06598, arXiv.org.
    4. 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.
    5. Francesco Menoncin & Elena Vigna, 2019. "Mean-variance dynamic optimality for DC pension schemes," Carlo Alberto Notebooks 587, Collegio Carlo Alberto.
    6. Alessandro Milazzo & Elena Vigna, 2018. "The Italian Pension Gap: a Stochastic Optimal Control Approach," Papers 1804.05354, arXiv.org.
    7. Li, Yuying & Forsyth, Peter A., 2019. "A data-driven neural network approach to optimal asset allocation for target based defined contribution pension plans," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 189-204.
    8. Alessandro Milazzo & Elena Vigna, 2018. "The Italian Pension Gap: A Stochastic Optimal Control Approach," Risks, MDPI, vol. 6(2), pages 1-20, April.
    9. Peter A. Forsyth & Kenneth R. Vetzal, 2019. "Defined Contribution Pension Plans: Who Has Seen the Risk?," JRFM, MDPI, vol. 12(2), pages 1-27, April.
    10. Pengyu Wei & Charles Yang, 2023. "Optimal investment for defined-contribution pension plans under money illusion," Review of Quantitative Finance and Accounting, Springer, vol. 61(2), pages 729-753, August.
    11. Alessandra Milazzo & Elena Vigna, 2018. "The Italian Pension Gap: a Stochastic Optimal Control Approach," Carlo Alberto Notebooks 553, Collegio Carlo Alberto.
    12. Alessandro Milazzo & Elena Vigna, 2018. "“The Italian Pension Gap: a Stochastic Optimal Control Approach"," CeRP Working Papers 179, Center for Research on Pensions and Welfare Policies, Turin (Italy).
    13. Forsyth, Peter A., 2022. "Short term decumulation strategies for underspending retirees," Insurance: Mathematics and Economics, Elsevier, vol. 102(C), pages 56-74.

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    More about this item

    Keywords

    Mean–variance approach; Defined contribution pension scheme; Stochastic optimal control; Martingale method; Efficient frontier; Ruin probability;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General
    • 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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