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Optimal asset allocation for pension funds under mortality risk during the accumulation and decumulation phases

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  • Paolo Battocchio
  • Francesco Menoncin
  • Olivier Scaillet

Abstract

In a financial market with one riskless asset and n risky assets following geometric Brownian motions, we solve the problem of a pension fund maximizing the expected CRRA utility of its terminal wealth. By considering a stochastic death time for a subscriber, we solve a unique problem for both accumulation and decumulation phases. We show that the optimal asset allocation during these two phases must be different. In particular, during the first phase the investment in the risky assets should decrease through time to meet future contractual pension payments while, during the second phase, the risky investment should increase through time because of closeness of death time. Our findings also suggest that it is not optimal to manage the two phases separately.
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Suggested Citation

  • Paolo Battocchio & Francesco Menoncin & Olivier Scaillet, 2003. "Optimal asset allocation for pension funds under mortality risk during the accumulation and decumulation phases," THEMA Working Papers 2003-28, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    • Handle: RePEc:ema:worpap:2003-28
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    Cited by:

    1. Marina Di Giacinto & Salvatore Federico & Fausto Gozzi, 2011. "Pension funds with a minimum guarantee: a stochastic control approach," Finance and Stochastics, Springer, vol. 15(2), pages 297-342, June.
    2. Chavez-Bedoya, Luis & Castaneda, Ranu, 2021. "A benchmarking approach to track and compare administrative charges on flow and balance in individual account pension systems," Insurance: Mathematics and Economics, Elsevier, vol. 97(C), pages 7-23.
    3. Oyakhilome IBHAGUI, 2017. "Optimal Asset Allocation of a Pension Fund: Does The Fear of Regret Matter?," Journal of Economics Library, KSP Journals, vol. 4(2), pages 130-159, June.
    4. Menoncin, Francesco, 2005. "Cyclical risk exposure of pension funds: A theoretical framework," Insurance: Mathematics and Economics, Elsevier, vol. 36(3), pages 469-484, June.
    5. Milevsky, Moshe A. & Young, Virginia R., 2007. "Annuitization and asset allocation," Journal of Economic Dynamics and Control, Elsevier, vol. 31(9), pages 3138-3177, September.
    6. Ankush Agarwal & Christian-Oliver Ewald & Yongjie Wang, 2023. "Hedging longevity risk in defined contribution pension schemes," Computational Management Science, Springer, vol. 20(1), pages 1-34, December.
    7. 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.
    8. Francesco Menoncin & Luca Regis, 2015. "Longevity assets and pre-retirement consumption/portfolio decisions," Working Papers 2/2015, IMT School for Advanced Studies Lucca, revised May 2015.
    9. Ayşegül İşcanog̃lu-Çekiç, 2016. "An Optimal Turkish Private Pension Plan with a Guarantee Feature," Risks, MDPI, vol. 4(3), pages 1-12, June.
    10. Josa-Fombellida, Ricardo & Rincón-Zapatero, Juan Pablo, 2012. "Stochastic pension funding when the benefit and the risky asset follow jump diffusion processes," European Journal of Operational Research, Elsevier, vol. 220(2), pages 404-413.
    11. Pierre Devolder & Susanna Levantesi & Massimiliano Menzietti, 2021. "Automatic balance mechanisms for notional defined contribution pension systems guaranteeing social adequacy and financial sustainability: an application to the Italian pension system," Annals of Operations Research, Springer, vol. 299(1), pages 765-795, April.
    12. Gerrard, Russell & Kyriakou, Ioannis & Nielsen, Jens Perch & Vodička, Peter, 2023. "On optimal constrained investment strategies for long-term savers in stochastic environments and probability hedging," European Journal of Operational Research, Elsevier, vol. 307(2), pages 948-962.
    13. Luciano, Elisa & Regis, Luca, 2014. "Efficient versus inefficient hedging strategies in the presence of financial and longevity (value at) risk," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 68-77.
    14. Menoncin, Francesco & Regis, Luca, 2017. "Longevity-linked assets and pre-retirement consumption/portfolio decisions," Insurance: Mathematics and Economics, Elsevier, vol. 76(C), pages 75-86.
    15. Schmeck, Maren Diane & Schmidli, Hanspeter, 2019. "Mortality Options: the Point of View of an Insurer," Center for Mathematical Economics Working Papers 616, Center for Mathematical Economics, Bielefeld University.
    16. Baltas, I. & Dopierala, L. & Kolodziejczyk, K. & Szczepański, M. & Weber, G.-W. & Yannacopoulos, A.N., 2022. "Optimal management of defined contribution pension funds under the effect of inflation, mortality and uncertainty," European Journal of Operational Research, Elsevier, vol. 298(3), pages 1162-1174.
    17. Jangho Park & Rebecca Stockbridge & Güzin Bayraksan, 2021. "Variance reduction for sequential sampling in stochastic programming," Annals of Operations Research, Springer, vol. 300(1), pages 171-204, May.
    18. Francesco Menoncin & Olivier Scaillet, 2003. "Mortality Risk and Real Optimal Asset Allocation for Pension Funds," FAME Research Paper Series rp101, International Center for Financial Asset Management and Engineering.
    19. Schmeck, Maren Diane & Schmidli, Hanspeter, 2021. "Mortality options: The point of view of an insurer," Insurance: Mathematics and Economics, Elsevier, vol. 96(C), pages 98-115.
    20. Mehmet BÖLÜKBAÞ, 2017. "18. International symposium on econometrics operation research and statistics," Journal of Economics Library, KSP Journals, vol. 4(3), pages 402-403, September.
    21. Le Courtois, Olivier & Menoncin, Francesco, 2015. "Portfolio optimisation with jumps: Illustration with a pension accumulation scheme," Journal of Banking & Finance, Elsevier, vol. 60(C), pages 127-137.
    22. Katarzyna Romaniuk, 2007. "The optimal asset allocation of the main types of pension funds: a unified framework," The Geneva Papers on Risk and Insurance Theory, Springer;International Association for the Study of Insurance Economics (The Geneva Association), vol. 32(2), pages 113-128, December.

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    JEL classification:

    • G23 - Financial Economics - - Financial Institutions and Services - - - Non-bank Financial Institutions; Financial Instruments; Institutional Investors
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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