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Optimal Pension Management under Stochastic Interest Rates, Wages, and Inflation

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  • Paolo BATTOCCHIO

    (UNIVERSITE CATHOLIQUE DE LOUVAIN, Institut de Recherches Economiques et Sociales (IRES))

  • Francesco MENONCIN

    (UNIVERSITE CATHOLIQUE DE LOUVAIN, Institut de Recherches Economiques et Sociales (IRES))

Abstract

We consider a stochastic model for a defined-contribution pension fund in continuous time. In particular, we focus on the portfolio problem of a fund manager who wants to maximize the expected utility of his terminal wealth in a complete financial market with stochastic interest rate. The fund manager must cope with two background risks: the salary risk and the inflation risk. We find a closed form solution for the asset allocation problem and so we are able to analyse in detail the behaviour of the optimal portfolio with respect to salary and inflation. Finally, a numerical simulation is presented.

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Bibliographic Info

Paper provided by Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES) in its series Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) with number 2002021.

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Length: 28
Date of creation: 01 Jun 2002
Date of revision:
Handle: RePEc:ctl:louvir:2002021

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Keywords: defined-contribution pension plan; salary risk; inflation risk; stochastic optimal control; Hamilton-Jacobi-Bellman equation;

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References

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  1. Campbell, John Y. & Viceira, Luis M., 2002. "Strategic Asset Allocation: Portfolio Choice for Long-Term Investors," OUP Catalogue, Oxford University Press, number 9780198296942.
  2. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
  3. Lioui, Abraham & Poncet, Patrice, 2001. "On optimal portfolio choice under stochastic interest rates," Journal of Economic Dynamics and Control, Elsevier, vol. 25(11), pages 1841-1865, November.
  4. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-92.
  5. Heath, David & Jarrow, Robert & Morton, Andrew, 1992. "Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation," Econometrica, Econometric Society, vol. 60(1), pages 77-105, January.
  6. 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 247-57, August.
  7. Cox, John C. & Huang, Chi-fu, 1991. "A variational problem arising in financial economics," Journal of Mathematical Economics, Elsevier, vol. 20(5), pages 465-487.
  8. Paolo Battocchio & Francesco Menoncin, 2002. "Optimal Portfolio Strategies with Stochastic Wage Income and Inflation: The Case of a Defined Contribution Pension Plan," CeRP Working Papers 19, Center for Research on Pensions and Welfare Policies, Turin (Italy).
  9. Blake, David & Cairns, Andrew J. G. & Dowd, Kevin, 2001. "Pensionmetrics: stochastic pension plan design and value-at-risk during the accumulation phase," Insurance: Mathematics and Economics, Elsevier, vol. 29(2), pages 187-215, October.
  10. Vigna, Elena & Haberman, Steven, 2001. "Optimal investment strategy for defined contribution pension schemes," Insurance: Mathematics and Economics, Elsevier, vol. 28(2), pages 233-262, April.
  11. Menoncin, Francesco, 2002. "Optimal portfolio and background risk: an exact and an approximated solution," Insurance: Mathematics and Economics, Elsevier, vol. 31(2), pages 249-265, October.
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Cited by:
  1. 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.
  2. Francesco, MENONCIN, 2003. "Optimal Real Consumption and Asset Allocation for a HARA Investor with Labour Income," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 2003015, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
  3. Zhang, Aihua & Korn, Ralf & Ewald, Christian-Oliver, 2007. "Optimal management and inflation protection for defined contribution pension plans," MPRA Paper 3300, University Library of Munich, Germany.

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