Work

Obstacle mean-field game problem

Year: 2015

Type: article

Abstract: In this paper, we introduce and study a first-order mean-field game obstacle problem. We examine the case of local dependence on the measure under assumptions that include both the logarithmic case and power-like nonlinearities. Since the obstacle operator is not differentiable, the equations for first-order mean field game problems have to be discussed carefully. Hence, we begin by considering a penalized problem. We prove this problem admits a unique solution satisfying uniform bounds. These bounds serve to pass to the limit in the penalized problem and to characterize the limiting equations. Finally, we prove uniqueness of solutions.

Source: Interfaces and Free Boundaries Mathematical Analysis Computation and Applications

DOI: 10.4171/ifb/333

Authors: Diogo A. Gomes, Stefania Patrizi

Institutions: King Abdullah University of Science and Technology, Weierstrass Institute for Applied Analysis and Stochastics

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: bronze

Funder: King Abdullah University of Science and Technology

OpenAlex ID: W224423923

FWCI: 11.47

Cites: 13

Cited by: 29

Related to: 10