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SIMULATING NUMERICALLY THE KRUSELL-SMITH MODEL WITH NEURAL NETWORKS

Abstract : The celebrated Krusel-Smith growth model is an important example of a Mean Field Game with a common noise. The Mean Field Game is encoded in the master equation, a partial differential equation satisfied by the value of the game which depends on the whole distribution of states. The latter equation is therefore posed in an infinite dimensional space. This makes the numerical simulations quite challenging. However, Krusell and Smith conjectured that the value function of the game mostly depends on the state distribution through low dimensional quantities. In this paper, we wish to propose a numerical method for approximating the solutions of the master equation arising in Krusell-Smith model, and for adaptively identifying low-dimensional variables which retain an important part of the information. This new numerical framework is based on a semi-Lagrangian method and uses neural networks as an important ingredient.
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Preprints, Working Papers, ... (Preprint)
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https://hal-cnrs.archives-ouvertes.fr/hal-03851542
Contributor : Yves Achdou Connect in order to contact the contributor
Submitted on : Monday, November 14, 2022 - 3:09:14 PM
Last modification on : Tuesday, November 15, 2022 - 3:55:50 AM

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Krusell_smith_v3.pdf
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  • HAL Id : hal-03851542, version 1
  • ARXIV : 2211.07698

Citation

Yves Achdou, Jean-Michel Lasry, Pierre Louis Lions. SIMULATING NUMERICALLY THE KRUSELL-SMITH MODEL WITH NEURAL NETWORKS. {date}. ⟨hal-03851542⟩

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