Article Dans Une Revue Probability Theory and Related Fields Année : 2011

Backward SDEs with superquadratic growth

Résumé

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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hal-00362685 , version 1 (19-02-2009)

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Freddy Delbaen, Ying Hu, Xiaobo Bao. Backward SDEs with superquadratic growth. Probability Theory and Related Fields, 2011, 150 (1-2), pp.145-192. ⟨10.1007/s00440-010-0271-1⟩. ⟨hal-00362685⟩
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