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Heterogeneous-Agent Models in Asset Pricing: The Dynamic Programming Approach and Finite Difference Method

Author

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  • Galindo Gil Hamilton

    (Department of Finance and Economics, Monte Ahuja College of Business, 2564 Cleveland State University , 1860 E 18th St, Cleveland, OH 44114, USA)

Abstract

This paper provides a detailed guide to solving a model characterized by risk-aversion heterogeneity, utilizing the dynamic programming approach in conjunction with the finite difference method. Although this model is characterized by a system of three partial differential equations (PDEs) – two related to the agents’ value functions and one to the risky asset price – it is surprisingly unnecessary to solve the full 3-PDEs system. Solving the 2-PDEs system for the agents’ value functions is sufficient, as, in equilibrium, the risky asset price is a function of these values. This problem is further simplified since each agent’s PDE can be solved independently due to the properties of the value function under constant relative risk aversion (CRRA) preferences. Finally, we demonstrate that applying the finite difference method with the implicit approach and an upwind scheme is straightforward for this type of asset pricing model.

Suggested Citation

  • Galindo Gil Hamilton, 2025. "Heterogeneous-Agent Models in Asset Pricing: The Dynamic Programming Approach and Finite Difference Method," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 25(1), pages 213-253.
    • Handle: RePEc:bpj:bejtec:v:25:y:2025:i:1:p:213-253:n:1005
    DOI: 10.1515/bejte-2024-0065
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    More about this item

    Keywords

    heterogeneous agents; preferences; asset pricing; dynamic programming; finite difference; continuous time;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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