Markovian quadratic and superquadratic BSDEs with an unbounded terminal condition

Adrien Richou 1, 2
2 ALEA - Advanced Learning Evolutionary Algorithms
Inria Bordeaux - Sud-Ouest, UB - Université de Bordeaux, CNRS - Centre National de la Recherche Scientifique : UMR5251
Abstract : This article deals with the existence and the uniqueness of solutions to quadratic and superquadratic Markovian backward stochastic differential equations (BSDEs for short) with an unbounded terminal condition. Our results are deeply linked with a strong a priori estimate on $Z$ that takes advantage of the Markovian framework. This estimate allows us to prove the existence of a viscosity solution to a semilinear parabolic partial differential equation with nonlinearity having quadratic or superquadratic growth in the gradient of the solution. This estimate also allows us to give explicit convergence rates for time approximation of quadratic or superquadratic Markovian BSDEs.
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Stochastic Processes and their Applications, Elsevier, 2012, 122 (9), pp.3173--3208. <10.1016/j.spa.2012.05.015>
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https://hal.archives-ouvertes.fr/hal-00643198
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Soumis le : jeudi 26 avril 2012 - 17:39:30
Dernière modification le : vendredi 11 septembre 2015 - 01:07:07
Document(s) archivé(s) le : vendredi 27 juillet 2012 - 02:36:57

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Adrien Richou. Markovian quadratic and superquadratic BSDEs with an unbounded terminal condition. Stochastic Processes and their Applications, Elsevier, 2012, 122 (9), pp.3173--3208. <10.1016/j.spa.2012.05.015>. <hal-00643198v2>

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