Solvability of Infinite horizon McKean-Vlasov FBSDEs in Mean Field Control Problems and Games
Erhan Bayraktar, Xin Zhang
TL;DR
This paper establishes existence and uniqueness results for infinite horizon McKean-Vlasov FBSDEs and applies these findings to solve mean field control problems and games.
Contribution
It introduces two methods for proving solvability of infinite horizon McKean-Vlasov FBSDEs under different assumptions, advancing mean field control and game theory.
Findings
Proved existence and uniqueness of solutions for infinite horizon McKean-Vlasov FBSDEs.
Applied these results to solve mean field control problems.
Applied these results to solve mean field games.
Abstract
In this paper, we show existence and uniqueness of solutions of the infinite horizon McKean-Vlasov FBSDEs using two different methods, which lead to two different sets of assumptions. We use these results to solve the infinite horizon mean field type control problems and mean field games.
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Taxonomy
TopicsStochastic processes and financial applications · Fluid Dynamics and Turbulent Flows · Navier-Stokes equation solutions