A class of globally solvable Markovian quadratic BSDE systems and applications

TL;DR

This paper proves existence and uniqueness for a broad class of Markovian quadratic BSDE systems under verifiable conditions, with applications in finance, game theory, and geometry.

Contribution

It introduces a new framework with structural assumptions ensuring solvability of quadratic BSDE systems, extending previous results.

Findings

Established existence and uniqueness for the class of systems.

Provided verifiable conditions for the assumptions.

Applied results to finance, game theory, and geometry.

Abstract

We establish existence and uniqueness for a wide class of Markovian systems of backward stochastic differential equations (BSDE) with quadratic nonlinearities. This class is characterized by an abstract structural assumption on the generator, an a-priori local-boundedness property, and a locally-H\"older-continuous terminal condition. We present easily verifiable sufficient conditions for these assumptions and treat several applications, including stochastic equilibria in incomplete financial markets, stochastic differential games, and martingales on Riemannian manifolds.