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Pareto Optimal Pension Risk Allocations

Author

Listed:
  • Sander Muns

    (Tilburg University)

  • Bas J. M. Werker

    (Tilburg University)

Abstract

We consider a funded pension system where collective risks, in a simple Black-Scholes financial market, are allocated to the retirement savings of individual participants. In particular, we consider an allocation in such a way that the relative effect on total retirement wealth, that is, the sum of financial wealth and human capital, is the same for each participant. We show that this allocation is Pareto efficient. This stylized life-cycle fact inspired the new Dutch retirement system. Subsequently, we extend the allocation rule to a setting that includes annuity risk. This risk can be a traded risk (e.g., interest rate risk) as well as a non-traded risk (e.g., longevity risk). From our closed-form solutions, we identify the similarities between our optimal allocation rule and the allocation rule in the new Dutch retirement system. A numerical example illustrates our findings.

Suggested Citation

  • Sander Muns & Bas J. M. Werker, 2022. "Pareto Optimal Pension Risk Allocations," De Economist, Springer, vol. 170(1), pages 133-172, February.
    • Handle: RePEc:kap:decono:v:170:y:2022:i:1:d:10.1007_s10645-022-09397-6
    DOI: 10.1007/s10645-022-09397-6
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    References listed on IDEAS

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    1. Servaas Bilsen & Roel J. Mehlkopf & Stephan Stalborch, 2022. "Intergenerational Transfers in the New Dutch Pension Contract," De Economist, Springer, vol. 170(1), pages 37-67, February.
    2. Bao, Hailong & Ponds, Eduard H.M. & Schumacher, Johannes M., 2017. "Multi-period risk sharing under financial fairness," Insurance: Mathematics and Economics, Elsevier, vol. 72(C), pages 49-66.
    3. Pazdera, Jaroslav & Schumacher, Johannes M. & Werker, Bas J.M., 2017. "The composite iteration algorithm for finding efficient and financially fair risk-sharing rules," Journal of Mathematical Economics, Elsevier, vol. 72(C), pages 122-133.
    4. Pazdera, Jaroslav & Schumacher, Johannes M. & Werker, Bas J.M., 2016. "Cooperative investment in incomplete markets under financial fairness," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 394-406.
    5. Paul A. Samuelson, 2011. "Lifetime Portfolio Selection by Dynamic Stochastic Programming," World Scientific Book Chapters, in: Leonard C MacLean & Edward O Thorp & William T Ziemba (ed.), THE KELLY CAPITAL GROWTH INVESTMENT CRITERION THEORY and PRACTICE, chapter 31, pages 465-472, World Scientific Publishing Co. Pte. Ltd..
    6. Bovenberg, A.L. & Koijen, R.S.J. & Nijman, T.E. & Teulings, C.N., 2007. "Saving and investing over the life cycle and the role of collective pension funds," Other publications TiSEM 6eab1341-eda5-4f21-8c06-8, Tilburg University, School of Economics and Management.
    7. Ralph S. J. Koijen & Theo E. Nijman & Bas J. M. Werker, 2011. "Optimal Annuity Risk Management," Review of Finance, European Finance Association, vol. 15(4), pages 799-833.
    8. Francisco Gomes, 2020. "Portfolio Choice Over the Life Cycle: A Survey," Annual Review of Financial Economics, Annual Reviews, vol. 12(1), pages 277-304, December.
    9. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    10. Luuk Metselaar & Peter Zwaneveld & Casper Ewijk, 2022. "Reforming Occupational Pensions in the Netherlands: Contract and Intergenerational Aspects," De Economist, Springer, vol. 170(1), pages 7-36, February.
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    Cited by:

    1. Servaas Bilsen & Roel J. Mehlkopf & Stephan Stalborch, 2022. "Intergenerational Transfers in the New Dutch Pension Contract," De Economist, Springer, vol. 170(1), pages 37-67, February.

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    More about this item

    Keywords

    Pension system; Funded pensions; Risk sharing; Risk allocation rules; Pareto optimality; Life-cycle investing;
    All these keywords.

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • J32 - Labor and Demographic Economics - - Wages, Compensation, and Labor Costs - - - Nonwage Labor Costs and Benefits; Retirement Plans; Private Pensions

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