## The Annals of Probability

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

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

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#### 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**

Received: March 2016

Revised: March 2017

First available in Project Euclid: 5 February 2018

**Permanent link to this document**

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

**Digital Object Identifier**

doi:10.1214/17-AOP1190

**Mathematical Reviews number (MathSciNet)**

MR3758736

**Zentralblatt MATH identifier**

06865128

**Subjects**

Primary: 60G44: Martingales with continuous parameter 60G99: None of the above, but in this section 60H30: Applications of stochastic analysis (to PDE, etc.)

Secondary: 58J65: Diffusion processes and stochastic analysis on manifolds [See also 35R60, 60H10, 60J60] 91A15: Stochastic games 91B51: Dynamic stochastic general equilibrium theory

**Keywords**

BSDE backward stochastic differential equations systems of BSDE quadratic nonlinearities stochastic equilibrium martingales on manifolds nonzero-sum stochastic games

#### 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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