The Annals of Probability

A class of globally solvable Markovian quadratic BSDE systems and applications

Hao Xing and Gordan Žitković

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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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