A class of globally solvable Markovian quadratic BSDE systems and applications

Hao Xing ^[1] ; Gordan Žitković ^[2]
1. [1] London School of Economics (UK)
2. [2] University of Texas (USA)
Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 46, Nº. 1, 2018, págs. 491-550
Idioma: inglés
DOI: 10.1214/17-AOP1190
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Resumen
- 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.