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Applications of Markov Chain Approximation Methods to Optimal Control Problems in Economics

Author

Listed:
  • Keyvan Eslami
  • Tom Phelan
Abstract
In this paper we explore some benefits of using the finite-state Markov chain approximation (MCA) method of Kushner and Dupuis (2001) to solve continuous-time optimal control problems in economics. We first show that the implicit finite-difference scheme of Achdou et al. (2022) amounts to a limiting form of the MCA method for a certain choice of approximating chains and policy function iteration for the resulting system of equations. We then illustrate that, relative to the implicit finite-difference approach, using variations of modified policy function iteration to solve income fluctuation problems both with and without discrete choices can lead to an increase in the speed of convergence of more than an order of magnitude. Finally, we provide several consistent chain constructions for stationary portfolio problems with correlated state variables, and illustrate the flexibility of the MCA approach by using it to construct and compare two simple solution methods for a general equilibrium model with financial frictions.

Suggested Citation

  • Keyvan Eslami & Tom Phelan, 2021. "Applications of Markov Chain Approximation Methods to Optimal Control Problems in Economics," Working Papers 21-04R, Federal Reserve Bank of Cleveland, revised 17 May 2022.
    • Handle: RePEc:fip:fedcwq:89860
    DOI: 10.26509/frbc-wp-202104r
    Note: Replication materials may be found at https://github.com/tphelanECON/EslamiPhelan_MCA
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    References listed on IDEAS

    as
    1. Daniel Barczyk & Matthias Kredler, 2014. "Altruistically motivated transfers under uncertainty," Quantitative Economics, Econometric Society, vol. 5(3), pages 705-749, November.
    2. Martin L. Puterman & Moon Chirl Shin, 1978. "Modified Policy Iteration Algorithms for Discounted Markov Decision Problems," Management Science, INFORMS, vol. 24(11), pages 1127-1137, July.
    3. Daniel Barczyk & Matthias Kredler, 2014. "A Dynamic Model of Altruistically-Motivated Transfers," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 17(2), pages 303-328, April.
    4. Daniel Barczyk & Matthias Kredler, 2014. "A Dynamic Model of Altruistically-Motivated Transfers," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 17(2), pages 303-328, April.
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    Cited by:

    1. Rendahl, Pontus, 2022. "Continuous vs. discrete time: Some computational insights," Journal of Economic Dynamics and Control, Elsevier, vol. 144(C).
    2. Keyvan Eslami & Tom Phelan, 2023. "The Art of Temporal Approximation An Investigation into Numerical Solutions to Discrete and Continuous-Time Problems in Economics," Working Papers 23-10, Federal Reserve Bank of Cleveland.

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    More about this item

    Keywords

    Dynamic programming; financial frictions; Numerical methods; Markov chain approximation;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • E00 - Macroeconomics and Monetary Economics - - General - - - General
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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