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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.

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Bibliographic Info

Article provided by Elsevier in its journal European Journal of Operational Research.

Volume (Year): 220 (2012)
Issue (Month): 2 ()
Pages: 404-413

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Handle: RePEc:eee:ejores:v:220:y:2012:i:2:p:404-413

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Web page: http://www.elsevier.com/locate/eor

Related research

Keywords: Optimization in financial mathematics; Pension funding; Stochastic control; Poisson process;

References

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  1. 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.
  2. Tomas Björk & Irina Slinko, 2006. "Towards a General Theory of Good-Deal Bounds," Review of Finance, European Finance Association, vol. 10(2), pages 221-260.
  3. 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.
  4. Chang, S. C. & Tzeng, Larry Y. & Miao, Jerry C. Y., 2003. "Pension funding incorporating downside risks," Insurance: Mathematics and Economics, Elsevier, vol. 32(2), pages 217-228, April.
  5. Zvi Bodie & Jay O. Light & Randall Morck & Robert A. Taggart, Jr., 1986. "Funding and Asset Allocation in Corporate Pension Plans: An Empirical Investigation," NBER Working Papers 1315, National Bureau of Economic Research, Inc.
  6. Berkelaar, Arjan & Kouwenberg, Roy, 2003. "Retirement saving with contribution payments and labor income as a benchmark for investments," Journal of Economic Dynamics and Control, Elsevier, vol. 27(6), pages 1069-1097, April.
  7. Ngwira, Bernard & Gerrard, Russell, 2007. "Stochastic pension fund control in the presence of Poisson jumps," Insurance: Mathematics and Economics, Elsevier, vol. 40(2), pages 283-292, March.
  8. 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.
  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. Wu, Liuren, 2003. " Jumps and Dynamic Asset Allocation," Review of Quantitative Finance and Accounting, Springer, vol. 20(3), pages 207-43, May.
  11. Haberman, Steven & Butt, Zoltan & Megaloudi, Chryssoula, 2000. "Contribution and solvency risk in a defined benefit pension scheme," Insurance: Mathematics and Economics, Elsevier, vol. 27(2), pages 237-259, October.
  12. Haberman, Steven & Sung, Joo-Ho, 1994. "Dynamic approaches to pension funding," Insurance: Mathematics and Economics, Elsevier, vol. 15(2-3), pages 151-162, December.
  13. Taylor, Greg, 2002. "Stochastic control of funding systems," Insurance: Mathematics and Economics, Elsevier, vol. 30(3), pages 323-350, June.
  14. 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.
  15. Haberman, Steven & Sung, Joo-Ho, 2005. "Optimal pension funding dynamics over infinite control horizon when stochastic rates of return are stationary," Insurance: Mathematics and Economics, Elsevier, vol. 36(1), pages 103-116, February.
  16. Josa-Fombellida, Ricardo & Rincon-Zapatero, Juan Pablo, 2001. "Minimization of risks in pension funding by means of contributions and portfolio selection," Insurance: Mathematics and Economics, Elsevier, vol. 29(1), pages 35-45, August.
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Cited by:
  1. Marina Di Giacinto & Salvatore Federico & Fausto Gozzi & Elena Vigna, 2012. "Income drawdown option with minimum guarantee," Carlo Alberto Notebooks 272, Collegio Carlo Alberto.

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