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Solving Consumption and Portfolio Choice Problems: The State Variable Decomposition Method

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  • Lorenzo Garlappi
  • Georgios Skoulakis

Abstract

We develop a new solution method for a broad class of discrete-time dynamic portfolio choice problems. The method efficiently approximates conditional expectations of the value function by using (i) a decomposition of the state variables into a component observable by the investor and a stochastic deviation; and (ii) a Taylor expansion of the value function. We illustrate the accuracy of the method in handling several realistic features of portfolio choice problems such as intermediate consumption, multiple assets, multiple state variables, portfolio constraints, non-time-separable preferences, and nonredundant endogenous state variables. We finally use the method to solve a realistic large-scale life-cycle portfolio choice and consumption problem with predictable expected returns and recursive preferences. The Author 2010. Published by Oxford University Press on behalf of The Society for Financial Studies. All rights reserved. For Permissions, please e-mail: journals.permissions@oxfordjournals.org., Oxford University Press.

Suggested Citation

  • Lorenzo Garlappi & Georgios Skoulakis, 2010. "Solving Consumption and Portfolio Choice Problems: The State Variable Decomposition Method," The Review of Financial Studies, Society for Financial Studies, vol. 23(9), pages 3346-3400.
    • Handle: RePEc:oup:rfinst:v:23:y:2010:i:9:p:3346-3400
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    File URL: http://hdl.handle.net/10.1093/rfs/hhq045
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    Cited by:

    1. Zhu, Yichen & Escobar-Anel, Marcos, 2022. "Polynomial affine approach to HARA utility maximization with applications to OrnsteinUhlenbeck 4/2 models," Applied Mathematics and Computation, Elsevier, vol. 418(C).
    2. 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.
    3. Roche, Hervé & Tompaidis, Stathis & Yang, Chunyu, 2013. "Why does junior put all his eggs in one basket? A potential rational explanation for holding concentrated portfolios," Journal of Financial Economics, Elsevier, vol. 109(3), pages 775-796.
    4. Rongju Zhang & Nicolas Langren'e & Yu Tian & Zili Zhu & Fima Klebaner & Kais Hamza, 2018. "Local Control Regression: Improving the Least Squares Monte Carlo Method for Portfolio Optimization," Papers 1803.11467, arXiv.org, revised Sep 2018.
    5. Marine Carrasco & N’Golo Koné, 2024. "Test for Trading Costs Effect in a Portfolio Selection Problem with Recursive Utility," Journal of Financial Econometrics, Oxford University Press, vol. 22(4), pages 908-953.
    6. Mertens, Thomas M. & Judd, Kenneth L., 2018. "Solving an incomplete markets model with a large cross-section of agents," Journal of Economic Dynamics and Control, Elsevier, vol. 91(C), pages 349-368.
    7. Mark Broadie & Weiwei Shen, 2016. "High-Dimensional Portfolio Optimization With Transaction Costs," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(04), pages 1-49, June.
    8. Yichen Zhu & Marcos Escobar-Anel & Matt Davison, 2023. "A Polynomial-Affine Approximation for Dynamic Portfolio Choice," Computational Economics, Springer;Society for Computational Economics, vol. 62(3), pages 1177-1213, October.
    9. Rongju Zhang & Nicolas Langren'e & Yu Tian & Zili Zhu & Fima Klebaner & Kais Hamza, 2016. "Dynamic portfolio optimization with liquidity cost and market impact: a simulation-and-regression approach," Papers 1610.07694, arXiv.org, revised Jun 2019.
    10. Pagnoncelli, Bernardo K. & Homem-de-Mello, Tito & Lagos, Guido & Castañeda, Pablo & García, Javier, 2024. "Solving constrained consumption–investment problems by decomposition algorithms," European Journal of Operational Research, Elsevier, vol. 319(1), pages 292-302.
    11. Huang, Huaxiong & Milevsky, Moshe A., 2016. "Longevity risk and retirement income tax efficiency: A location spending rate puzzle," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 50-62.
    12. Mark Broadie & Weiwei Shen, 2017. "Numerical solutions to dynamic portfolio problems with upper bounds," Computational Management Science, Springer, vol. 14(2), pages 215-227, April.

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