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A Stochastic Model of Dynamic Consumption and Portfolio Decisions

Author

Listed:
  • Willi Semmler

    (New School University
    ZEW Mannheim and CEM Bielefeld University)

  • Maik Mueller

    (University of Bayreuth)

Abstract

This paper sets out a basic framework for solving a stochastic portfolio problem using dynamic programming (DP). Dynamic portfolio decisions are concerned with simultaneous decisions on savings and asset allocation whereby asset returns, such as on equity and bonds, are stochastic as in Campbell and Viceira (Strategic asset allocation, portfolio choice for long-term investors, 2002). In contrast to CV (2002) we do not use a local approximation method to solve the stochastic model but rather use a global solution procedure such as DP. Whereas CV (2002) solve their model by assuming a constant consumption-wealth ratio and equity premium, we can allow both to be time varying. Different variances of equity and bond returns are explored in their impact on saving and asset allocation decisions and on the value function. The stochastic dynamic portfolio decision method proposed here allows for online decisions as data on asset returns are available in real time. The method is set up in a way such that it also helps to make fund decisions online for various types of investment opportunities.

Suggested Citation

  • Willi Semmler & Maik Mueller, 2016. "A Stochastic Model of Dynamic Consumption and Portfolio Decisions," Computational Economics, Springer;Society for Computational Economics, vol. 48(2), pages 225-251, August.
    • Handle: RePEc:kap:compec:v:48:y:2016:i:2:d:10.1007_s10614-015-9517-4
    DOI: 10.1007/s10614-015-9517-4
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    References listed on IDEAS

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    1. Wachter, Jessica A., 2002. "Portfolio and Consumption Decisions under Mean-Reverting Returns: An Exact Solution for Complete Markets," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 37(1), pages 63-91, March.
    2. Willi Semmler, 2011. "Asset Prices, Booms and Recessions," Springer Books, Springer, number 978-3-642-20680-1, July.
    3. Campbell, John Y. & Viceira, Luis M., 2002. "Strategic Asset Allocation: Portfolio Choice for Long-Term Investors," OUP Catalogue, Oxford University Press, number 9780198296942.
    4. John H. Cochrane (ed.), 2006. "Financial Markets and the Real Economy," Books, Edward Elgar Publishing, number 2923.
    5. Munk, Claus & Sorensen, Carsten & Nygaard Vinther, Tina, 2004. "Dynamic asset allocation under mean-reverting returns, stochastic interest rates, and inflation uncertainty: Are popular recommendations consistent with rational behavior?," International Review of Economics & Finance, Elsevier, vol. 13(2), pages 141-166.
    Full references (including those not matched with items on IDEAS)

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