## The Annals of Probability

### A class of globally solvable Markovian quadratic BSDE systems and applications

#### 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-Hölder-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.

#### Article information

Source
Ann. Probab., Volume 46, Number 1 (2018), 491-550.

Dates
Revised: March 2017
First available in Project Euclid: 5 February 2018

https://projecteuclid.org/euclid.aop/1517821228

Digital Object Identifier
doi:10.1214/17-AOP1190

Mathematical Reviews number (MathSciNet)
MR3758736

Zentralblatt MATH identifier
06865128

#### Citation

Xing, Hao; Žitković, Gordan. A class of globally solvable Markovian quadratic BSDE systems and applications. Ann. Probab. 46 (2018), no. 1, 491--550. doi:10.1214/17-AOP1190. https://projecteuclid.org/euclid.aop/1517821228

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