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January 2018 A class of globally solvable Markovian quadratic BSDE systems and applications
Hao Xing, Gordan Žitković
Ann. Probab. 46(1): 491-550 (January 2018). DOI: 10.1214/17-AOP1190


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.


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Hao Xing. Gordan Žitković. "A class of globally solvable Markovian quadratic BSDE systems and applications." Ann. Probab. 46 (1) 491 - 550, January 2018.


Received: 1 March 2016; Revised: 1 March 2017; Published: January 2018
First available in Project Euclid: 5 February 2018

zbMATH: 06865128
MathSciNet: MR3758736
Digital Object Identifier: 10.1214/17-AOP1190

Primary: 60G44 , 60G99 , 60H30
Secondary: 58J65 , 91A15 , 91B51

Keywords: Backward stochastic differential equations , BSDE , martingales on manifolds , nonzero-sum stochastic games , quadratic nonlinearities , stochastic equilibrium , systems of BSDE

Rights: Copyright © 2018 Institute of Mathematical Statistics


Vol.46 • No. 1 • January 2018
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