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


  • Paolo Battocchio

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

  • Francesco Menoncin

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


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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    References listed on IDEAS

    1. Justine Hastings & Olivia S. Mitchell, 2010. "How Financial Literacy and Impatience Shape Retirement Wealth and Investment Behaviors," Working Papers wp233, University of Michigan, Michigan Retirement Research Center.
    2. Annamaria Lusardi & Jason Beeler, 2006. "Savings Between Cohorts: The Role of Planning," Working Papers wp122, University of Michigan, Michigan Retirement Research Center.
    3. Annamaria Lusardi & Olivia S. Mitchell, 2008. "Planning and Financial Literacy: How Do Women Fare?," American Economic Review, American Economic Association, vol. 98(2), pages 413-417, May.
    4. Lusardi, Annamaria & Tufano, Peter, 2015. "Debt literacy, financial experiences, and overindebtedness," Journal of Pension Economics and Finance, Cambridge University Press, vol. 14(04), pages 332-368, October.
    5. Annamaria Lusardi & Olivia S. Mitchell & Vilsa Curto, 2009. "Financial Literacy among the Young," Working Papers wp191, University of Michigan, Michigan Retirement Research Center.
    6. John Ameriks & Andrew Caplin & John Leahy, 2003. "Wealth Accumulation and the Propensity to Plan," The Quarterly Journal of Economics, Oxford University Press, vol. 118(3), pages 1007-1047.
    7. van Rooij, Maarten & Lusardi, Annamaria & Alessie, Rob, 2011. "Financial literacy and stock market participation," Journal of Financial Economics, Elsevier, vol. 101(2), pages 449-472, August.
    8. Christelis, Dimitris & Jappelli, Tullio & Padula, Mario, 2010. "Cognitive abilities and portfolio choice," European Economic Review, Elsevier, vol. 54(1), pages 18-38, January.
    9. Lusardi, Annamaria & Mitchell, Olivia S., 2007. "Baby Boomer retirement security: The roles of planning, financial literacy, and housing wealth," Journal of Monetary Economics, Elsevier, vol. 54(1), pages 205-224, January.
    10. Annamaria Lusardi & Olivia S. Mitchell, 2017. "How Ordinary Consumers Make Complex Economic Decisions: Financial Literacy and Retirement Readiness," Quarterly Journal of Finance (QJF), World Scientific Publishing Co. Pte. Ltd., vol. 7(03), pages 1-31, September.
    11. Annamaria Lusardi & Olivia S Mitchelli, 2007. "Financial Literacy and Retirement Preparedness: Evidence and Implications for Financial Education," Business Economics, Palgrave Macmillan;National Association for Business Economics, vol. 42(1), pages 35-44, January.
    12. Adele Atkinson & Stephen McKay & Sharon Collard & Elaine Kempson, 2007. "Levels of Financial Capability in the UK," Public Money & Management, Taylor & Francis Journals, vol. 27(1), pages 29-36, February.
    13. Jere R. Behrman & Olivia S. Mitchell & Cindy Soo & David Bravo, 2010. "Financial Literacy, Schooling, and Wealth Accumulation," NBER Working Papers 16452, National Bureau of Economic Research, Inc.
    14. James Banks & Zoe Oldfield, 2007. "Understanding Pensions: Cognitive Function, Numerical Ability and Retirement Saving," Fiscal Studies, Institute for Fiscal Studies, vol. 28(2), pages 143-170, June.
    15. Jingjing Chai & Wolfram Horneff & Raimond Maurer & Olivia S. Mitchell, 2009. "Extending Life Cycle Models of Optimal Portfolio Choice: Integrating Flexible Work, Endogenous Retirement, and Investment Decisions with Lifetime Payouts," Working Papers wp204, University of Michigan, Michigan Retirement Research Center.
    16. Annamaria Lusardi & Olivia Mitchell, 2007. "Financial Literacy and Retirement Planning: New Evidence from the Rand American Life Panel," Working Papers wp157, University of Michigan, Michigan Retirement Research Center.
    17. Annamaria Lusardi, 2008. "Household Saving Behavior: The Role of Financial Literacy, Information, and Financial Education Programs," NBER Working Papers 13824, National Bureau of Economic Research, Inc.
    18. Annamaria Lusardi, 2011. "Americans' Financial Capability," NBER Working Papers 17103, National Bureau of Economic Research, Inc.
    19. John Ameriks & Andrew Caplin & John Leahy, 2002. "Wealth Accumulation and the Propensity to Plan," NBER Working Papers 8920, National Bureau of Economic Research, Inc.
    20. Justine S. Hastings & Lydia Tejeda-Ashton, 2008. "Financial Literacy, Information, and Demand Elasticity: Survey and Experimental Evidence from Mexico," NBER Working Papers 14538, National Bureau of Economic Research, Inc.
    21. Annamaria Lusardi & Olivia S. Mitchell & Vilsa Curto, 2009. "Financial Literacy and Financial Sophistication Among Older Americans," NBER Working Papers 15469, National Bureau of Economic Research, Inc.
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    Cited by:

    1. Paolo BATTOCCHIO & Francesco MENONCIN, 2002. "Optimal Pension Management under Stochastic Interest Rates, Wages, and Inflation," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 2002021, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    2. 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


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

    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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