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Mean-variance dynamic optimality for DC pension schemes

Author

Listed:
  • Francesco Menoncin
  • Elena Vigna

Abstract

It is well known that the mean-variance portfolio selection is a time-inconsistent optimization problem. In the current literature, this time inconsistency is often tackled with either a game theoretical approach (Basak and Chabakauri, 2010, and Björk and Murgoci, 2010) or a so-called precommitment approach (Zhou and Li, 2000). The framework of a defined contribution (DC) pension scheme, which we deal with in this work, makes no exception, with a number of papers computing either the Nash equilibrium or the precommitment strategy in the presence of a variety of financial markets. Here, we solve a mean-variance portfolio selection problem for a DC pension fund through the dynamically optimal approach introduced by Pedersen and Peskir (2017), and we compare the dynamically optimal strategy with the precommitment one. We show that both strategies are the solution to target-based problems. The precommitment strategy has a constant target, while the dynamically optimal strategy has a time-varying target whose expectation coincides with the constant target of the previous case. We also show that the expected wealth is the same under the two approaches. Numerical simulations show that, with respect to the precommitment strategy, the dynamically optimal strategy provides: (i) a larger variance of wealth, (ii) a less volatile asset allocation, and (iii) a larger effectiveness in reacting against most unfavorable and persistent market conditions.

Suggested Citation

  • Francesco Menoncin & Elena Vigna, 2019. "Mean-variance dynamic optimality for DC pension schemes," Carlo Alberto Notebooks 587, Collegio Carlo Alberto.
    • Handle: RePEc:cca:wpaper:587
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    References listed on IDEAS

    as
    1. R. A. Pollak, 1968. "Consistent Planning," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 35(2), pages 201-208.
    2. 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.
    3. Tomas Björk & Mariana Khapko & Agatha Murgoci, 2017. "On time-inconsistent stochastic control in continuous time," Finance and Stochastics, Springer, vol. 21(2), pages 331-360, April.
    4. Suleyman Basak & Georgy Chabakauri, 2010. "Dynamic Mean-Variance Asset Allocation," The Review of Financial Studies, Society for Financial Studies, vol. 23(8), pages 2970-3016, August.
    5. Elena Vigna, 2014. "On efficiency of mean--variance based portfolio selection in defined contribution pension schemes," Quantitative Finance, Taylor & Francis Journals, vol. 14(2), pages 237-258, February.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Time inconsistency; dynamic programming; martingale approach; pre commitment approach; mean-variance portfolio selection.;
    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
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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