Electron. J. Diff. Equ., Vol. 2011 (2011), No. 110, pp. 1-6.

Comparison and existence theorems for backwards stochastic DE's with discontinuous generators

Nikolaos Halidias, Peter E. Kloeden

An existence result is proved for backwards stochastic differential equations (BSDEs) with a generator f(t,x,z) which is possibly discontinuous in the x variable. For this comparison results are first established for BSDEs with the generator satisfying a generalized Lipschitz condition in its x variable.

Submitted May 25, 2010. Published August 26, 2011.
Math Subject Classifications: 60H10, 60H20.
Key Words: Backward stochastic differentail equation; comparison theorem; discontinuous generator.

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Nikolaos Halidias
Department of Statistics and Actuarial-Financial Mathematics
University of the Aegean
Karlovassi 83200 Samos, Greece
email: nick@aegean.gr
Peter E. Kloeden
Institut für Mathematik, Goethe-Universität
D-60054 Frankfurt am Main, Germany
email: kloeden@math.uni-frankfurt.de

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