A mean field game price model with noise

Diogo Gomes; Julian Gutierrez; Ricardo Ribeiro; Diogo Gomes; Julian Gutierrez; Ricardo Ribeiro

doi:10.3934/mine.2021028

Mathematics in Engineering

2021, Volume 3, Issue 4: 1-14. doi: 10.3934/mine.2021028

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A mean field game price model with noise

1.
CEMSE Division, King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia
2.
Departamento Acadêmico de Matemática, Universidade Tecnológica Federal do Paraná (UTFPR), Londrina, PR, Brazil

Received: 02 March 2020 Accepted: 23 May 2020 Published: 27 July 2020

Abstract
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In this paper, we propose a mean-field game model for the price formation of a commodity whose production is subjected to random fluctuations. The model generalizes existing deterministic price formation models. Agents seek to minimize their average cost by choosing their trading rates with a price that is characterized by a balance between supply and demand. The supply and the price processes are assumed to follow stochastic differential equations. Here, we show that, for linear dynamics and quadratic costs, the optimal trading rates are determined in feedback form. Hence, the price arises as the solution to a stochastic differential equation, whose coefficients depend on the solution of a system of ordinary differential equations.
- mean field games,
- price formation,
- common noise,
- linear quadratic model,
- constrained mean-field games,
- equilibrium pricing
Citation: Diogo Gomes, Julian Gutierrez, Ricardo Ribeiro. A mean field game price model with noise[J]. Mathematics in Engineering, 2021, 3(4): 1-14. doi: 10.3934/mine.2021028

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Abstract

In this paper, we propose a mean-field game model for the price formation of a commodity whose production is subjected to random fluctuations. The model generalizes existing deterministic price formation models. Agents seek to minimize their average cost by choosing their trading rates with a price that is characterized by a balance between supply and demand. The supply and the price processes are assumed to follow stochastic differential equations. Here, we show that, for linear dynamics and quadratic costs, the optimal trading rates are determined in feedback form. Hence, the price arises as the solution to a stochastic differential equation, whose coefficients depend on the solution of a system of ordinary differential equations.

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