A mean-field price model

Abstract: We propose a mean-field game model for the price formation of a commodity whose production is subjected to deterministic or random fluctuations. 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. In the deterministic case, we establish the existence of a solution under general conditions and give a full characterization. In the stochastic case, 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.

analysis of PDEs

Audience: researchers in the topic

Rio de Janeiro webinar on analysis and partial differential equations

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