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Optimal Portfolio Strategies with Stochastic Wage Income and Inflation: The Case of a Defined Contribution Pension Plan

Author

Listed:
  • Paolo Battocchio

    (Università degli Studi di Trieste, Dipartimento di Matematica Applicata)

  • Francesco Menoncin

    (Université Catholique de Louvain, IRES (Institut de Recherches Economiques et Sociales))

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 a set of stochastic investment opportunities and two background risks: the salary risk and the inflation risk. We use the stochastic dynamic programming approach. We show that the presence of the inflation risk can solve some problems linked to the use of the stochastic dynamic programming technique, and namely to the stochastic partial differential equation deriving from it. We find a closed form solution to the asset allocation problem, without specifying any functional form for the coe±cients of the diffusion processes involved in the problem. Finally, the derivation of a closed form solution allows us to analyse in detail the behaviour of the optimal portfolio with respect to salary and inflation.

Suggested Citation

  • 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).
    • Handle: RePEc:crp:wpaper:19
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    Citations

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    Cited by:

    1. Zhiping Chen & Liyuan Wang & Ping Chen & Haixiang Yao, 2019. "Continuous-Time Mean–Variance Optimization For Defined Contribution Pension Funds With Regime-Switching," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(06), pages 1-33, September.
    2. Huiling Wu, 2016. "Optimal Investment-Consumption Strategy under Inflation in a Markovian Regime-Switching Market," Discrete Dynamics in Nature and Society, Hindawi, vol. 2016, pages 1-17, July.
    3. 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).
    4. Battocchio, Paolo & Menoncin, Francesco, 2004. "Optimal pension management in a stochastic framework," Insurance: Mathematics and Economics, Elsevier, vol. 34(1), pages 79-95, February.

    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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