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Backward SDEs with superquadratic growth

Abstract : In this paper, we discuss the solvability of backward stochastic differential equations (BSDEs) with superquadratic generators. We first prove that given a superquadratic generator, there exists a bounded terminal value, such that the associated BSDE does not admit any bounded solution. On the other hand, we prove that if the superquadratic BSDE admits a bounded solution, then there exist infinitely many bounded solutions for this BSDE. Finally, we prove the existence of a solution for Markovian BSDEs where the terminal value is a bounded continuous function of a forward stochastic differential equation.
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Contributor : Ying Hu <>
Submitted on : Thursday, February 19, 2009 - 8:56:29 AM
Last modification on : Thursday, January 7, 2021 - 4:20:02 PM
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Freddy Delbaen, Ying Hu, Xiaobo Bao. Backward SDEs with superquadratic growth. Probability Theory and Related Fields, Springer Verlag, 2011, 150 (1-2), pp.145-192. ⟨10.1007/s00440-010-0271-1⟩. ⟨hal-00362685⟩



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