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

Author

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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.

Suggested Citation

  • Paolo BATTOCCHIO & Francesco MENONCIN, 2002. "Optimal Pension Management under Stochastic Interest Rates, Wages, and Inflation," LIDAM Discussion Papers IRES 2002021, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    • Handle: RePEc:ctl:louvir:2002021
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    References listed on IDEAS

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    1. 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).
    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. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," The Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-592.
    4. Paolo BATTOCCHIO, 2002. "Optimal Portfolio Strategies with Stochastic Wage Income : The Case of A defined Contribution Pension Plan," LIDAM Discussion Papers IRES 2002005, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    5. Campbell, John Y. & Viceira, Luis M., 2002. "Strategic Asset Allocation: Portfolio Choice for Long-Term Investors," OUP Catalogue, Oxford University Press, number 9780198296942.
    6. 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.
    7. 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.
    8. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305, World Scientific Publishing Co. Pte. Ltd..
    9. 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.
    10. 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.
    11. 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.
    12. Griselda Deelstra & Martino Grasselli & Pierre-François Koehl, 2000. "Optimal investment strategies in a CIR framework," ULB Institutional Repository 2013/7594, ULB -- Universite Libre de Bruxelles.
    13. 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.
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    Cited by:

    1. 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.
    2. Paolo Battocchio & Francesco Menoncin & Olivier Scaillet, 2007. "Optimal asset allocation for pension funds under mortality risk during the accumulation and decumulation phases," Annals of Operations Research, Springer, vol. 152(1), pages 141-165, July.
    3. Francesco, MENONCIN, 2003. "Optimal Real Consumption and Asset Allocation for a HARA Investor with Labour Income," LIDAM Discussion Papers IRES 2003015, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    4. 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.

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    More about this item

    Keywords

    defined-contribution pension plan; salary risk; inflation risk; stochastic optimal control; Hamilton-Jacobi-Bellman equation;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G23 - Financial Economics - - Financial Institutions and Services - - - Non-bank Financial Institutions; Financial Instruments; Institutional Investors

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