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Solving Constrained Consumption-Investment Problems by Simulation of Artificial Market Strategies

Author

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  • Björn Bick

    (Department of Finance, Goethe University Frankfurt am Main, 60323 Frankfurt am Main, Germany)

  • Holger Kraft

    (Department of Finance, Goethe University Frankfurt am Main, 60323 Frankfurt am Main, Germany)

  • Claus Munk

    (Department of Finance, Copenhagen Business School, DK-2000 Frederiksberg, Denmark)

Abstract

Utility-maximizing consumption and investment strategies in closed form are unknown for realistic settings involving portfolio constraints, incomplete markets, and potentially a high number of state variables. Standard numerical methods are hard to implement in such cases. We propose a numerical procedure that combines the abstract idea of artificial, unconstrained complete markets, well-known closed-form solutions in affine or quadratic return models, straightforward Monte Carlo simulation, and a standard iterative optimization routine. Our method provides an upper bound on the wealth-equivalent loss compared to the unknown optimal strategy, and it facilitates our understanding of the economic forces at play by building on closed-form expressions for the strategies considered. We illustrate and test our method on the life-cycle problem of an individual who receives unspanned labor income and cannot borrow or short sell. The upper loss bound is small, and our method performs well in comparison with two existing methods. This paper was accepted by Wei Xiong, finance.

Suggested Citation

  • Björn Bick & Holger Kraft & Claus Munk, 2013. "Solving Constrained Consumption-Investment Problems by Simulation of Artificial Market Strategies," Management Science, INFORMS, vol. 59(2), pages 485-503, June.
  • Handle: RePEc:inm:ormnsc:v:59:y:2013:i:2:p:485-503
    DOI: 10.1287/mnsc.1120.1623
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Kraft, Holger & Munk, Claus & Weiss, Farina, 2019. "Predictors and portfolios over the life cycle," Journal of Banking & Finance, Elsevier, vol. 100(C), pages 1-27.
    2. Hong, Yi & Jin, Xing, 2018. "Semi-analytical solutions for dynamic portfolio choice in jump-diffusion models and the optimal bond-stock mix," European Journal of Operational Research, Elsevier, vol. 265(1), pages 389-398.
    3. Lorenzo Reus & Frank J. Fabozzi, 2021. "Robust Solutions to the Life-Cycle Consumption Problem," Computational Economics, Springer;Society for Computational Economics, vol. 57(2), pages 481-499, February.
    4. Kasper Larsen & Oleksii Mostovyi & Gordan Žitković, 2018. "An expansion in the model space in the context of utility maximization," Finance and Stochastics, Springer, vol. 22(2), pages 297-326, April.
    5. Castañeda, Pablo & Reus, Lorenzo, 2019. "Suboptimal investment behavior and welfare costs: A simulation based approach," Finance Research Letters, Elsevier, vol. 30(C), pages 170-180.
    6. Thijs Kamma & Antoon Pelsser, 2019. "Near-Optimal Dynamic Asset Allocation in Financial Markets with Trading Constraints," Papers 1906.12317, arXiv.org, revised Oct 2019.
    7. Davi Valladão & Thuener Silva & Marcus Poggi, 2019. "Time-consistent risk-constrained dynamic portfolio optimization with transactional costs and time-dependent returns," Annals of Operations Research, Springer, vol. 282(1), pages 379-405, November.
    8. Farina Weiss, 2021. "A numerical approach to solve consumption-portfolio problems with predictability in income, stock prices, and house prices," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 93(1), pages 33-81, February.
    9. Kasper Larsen & Oleksii Mostovyi & Gordan v{Z}itkovi'c, 2014. "An expansion in the model space in the context of utility maximization," Papers 1410.0946, arXiv.org, revised Aug 2016.
    10. Munk, Claus, 2020. "A mean-variance benchmark for household portfolios over the life cycle," Journal of Banking & Finance, Elsevier, vol. 116(C).
    11. Paolo Guasoni & Gu Wang, 2020. "Consumption in incomplete markets," Finance and Stochastics, Springer, vol. 24(2), pages 383-422, April.
    12. Hambel, Christoph & Kraft, Holger & Meyer-Wehmann, André, 2020. "When should retirees tap their home equity?," SAFE Working Paper Series 293, Leibniz Institute for Financial Research SAFE.
    13. Wei-Ting Pan, 2016. "The Impact of Mandatory Savings on Life Cycle Consumption and Portfolio Choice," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 2-2016.

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