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Stochastic pension funding when the benefit and the risky asset follow jump diffusion processes

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  • Josa-Fombellida, Ricardo
  • Rincón-Zapatero, Juan Pablo

Abstract

We study the asset allocation of defined benefit pension plans of the type designed and sponsored by firms with the aim of providing a lifetime pension to the employees at the age of retirement. Benefits are stochastic, combining Poisson jumps with Brownian uncertainty. The sponsor dynamically forms portfolios where the risky asset is also subjected to Poisson jumps and Brownian uncertainty, possibly correlated with the evolution of benefits. The objective is to assure future benefits, while controlling the contribution made to the fund reserves. The problem is solved analytically using dynamic programming techniques.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:ejores:v:220:y:2012:i:2:p:404-413
    DOI: 10.1016/j.ejor.2012.01.033
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    References listed on IDEAS

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    1. Josa-Fombellida, Ricardo & Rincón-Zapatero, Juan Pablo, 2010. "Optimal asset allocation for aggregated defined benefit pension funds with stochastic interest rates," European Journal of Operational Research, Elsevier, vol. 201(1), pages 211-221, February.
    2. Sennewald, Ken, 2007. "Controlled stochastic differential equations under Poisson uncertainty and with unbounded utility," Journal of Economic Dynamics and Control, Elsevier, vol. 31(4), pages 1106-1131, April.
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    8. Chang, Shih-Chieh, 1999. "Optimal pension funding through dynamic simulations: the case of Taiwan public employees retirement system," Insurance: Mathematics and Economics, Elsevier, vol. 24(3), pages 187-199, May.
    9. Josa-Fombellida, Ricardo & Rincon-Zapatero, Juan Pablo, 2004. "Optimal risk management in defined benefit stochastic pension funds," Insurance: Mathematics and Economics, Elsevier, vol. 34(3), pages 489-503, June.
    10. Taylor, Greg, 2002. "Stochastic control of funding systems," Insurance: Mathematics and Economics, Elsevier, vol. 30(3), pages 323-350, June.
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    14. Josa-Fombellida, Ricardo & Rincon-Zapatero, Juan Pablo, 2008. "Mean-variance portfolio and contribution selection in stochastic pension funding," European Journal of Operational Research, Elsevier, vol. 187(1), pages 120-137, May.
    15. Cairns, Andrew, 2000. "Some Notes on the Dynamics and Optimal Control of Stochastic Pension Fund Models in Continuous Time," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 30(01), pages 19-55, May.
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    Cited by:

    1. Hainaut, Donatien, 2014. "Impulse control of pension fund contributions, in a regime switching economy," European Journal of Operational Research, Elsevier, vol. 239(3), pages 810-819.
    2. Di Giacinto, Marina & Federico, Salvatore & Gozzi, Fausto & Vigna, Elena, 2014. "Income drawdown option with minimum guarantee," European Journal of Operational Research, Elsevier, vol. 234(3), pages 610-624.
    3. 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.
    4. Castellano, Rosella & Cerqueti, Roy & Spinesi, Luca, 2016. "Sustainable management of fossil fuels: A dynamic stochastic optimization approach with jump-diffusion," European Journal of Operational Research, Elsevier, vol. 255(1), pages 288-297.
    5. repec:eee:insuma:v:76:y:2017:i:c:p:172-184 is not listed on IDEAS
    6. Ayşegül İşcanog̃lu-Çekiç, 2016. "An Optimal Turkish Private Pension Plan with a Guarantee Feature," Risks, MDPI, Open Access Journal, vol. 4(3), pages 1-12, June.
    7. Sun, Jingyun & Li, Zhongfei & Zeng, Yan, 2016. "Precommitment and equilibrium investment strategies for defined contribution pension plans under a jump–diffusion model," Insurance: Mathematics and Economics, Elsevier, vol. 67(C), pages 158-172.
    8. Francesco Menoncin & Elena Vigna, 2013. "Mean-variance target-based optimisation in DC plan with stochastic interest rate," Carlo Alberto Notebooks 337, Collegio Carlo Alberto.

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