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| HAL: hal-00643198, version 2 |
| arXiv: 1111.5137 |
| DOI: 10.1016/j.spa.2012.05.015 |
| Detailed view |  Export this paper |
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| Stochastic Processes and their Applications 122, 9 (2012) 3173--3208 |
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| Available versions: | v1 (2011-11-22) | v2 (2012-04-26) |
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| Markovian quadratic and superquadratic BSDEs with an unbounded terminal condition |
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| Adrien Richou 1, 2 |
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| (2012-09) |
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| 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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| 1: | Institut de Mathématiques de Bordeaux (IMB) |
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CNRS : UMR5251 – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II |
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| 2: | ALEA (INRIA Bordeaux - Sud-Ouest) |
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INRIA – Université de Bordeaux – CNRS : UMR5251 |
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| Subject | : | Mathematics/Probability |
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| hal-00643198, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00643198 | |
| oai:hal.archives-ouvertes.fr:hal-00643198 | |
| From: Adrien Richou | |
| Submitted on: Thursday, 26 April 2012 17:39:30 | |
| Updated on: Thursday, 22 November 2012 17:02:02 | |
