Year: 2025
Type: preprint
Abstract: Motivated by parallels between mean field games and random matrix theory, we develop stochastic optimal control problems and viscosity solutions to Hamilton-Jacobi equations in the setting of non-commutative variables. Rather than real vectors, the inputs to the equation are tuples of self-adjoint operators from a tracial von Neumann algebra. The individual noise from mean field games is replaced by a free semi-circular Brownian motion, which describes the large-$n$ limit of Brownian motion on the space of self-adjoint matrices. We introduce a classical common noise from mean field games into the non-commutative setting as well, allowing the problems to combine both classical and non-commutative randomness.
Source: arXiv (Cornell University)
Authors: Gangbo, Wilfrid, Jekel, David, Nam, Kyeongsik, Palmer, Aaron Z.
Language: English
Subfield: Finance
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W4414849792
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