Fixed point technique for a class of backward stochastic differential equations

Volume 6, Issue 1, pp 41--50 http://dx.doi.org/10.22436/jnsa.006.01.07

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Authors

Romeo Negrea - Department of Mathematics, Politehnica University of Timisoara, P-ta Victoriei 2, Timisoara, 300006, Romania. Ciprian Preda - Faculty of Economics and Business Administration, West University of Timisoara, Bd. V. Parvan 4, Timisoara, 300223, Romania.

Abstract

We establish a new theorem on the existence and uniqueness of the adapted solution to backward stochastic differential equations under some weaker conditions than the Lipschitz one. The extension is based on Athanassov's condition for ordinary differential equations. In order to prove the existence of the solutions we use a fixed point technique based on Schauder's fixed point theorem. Also, we study some regularity properties of the solution for this class of stochastic differential equations.

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Keywords

• Backward stochastic differential equations
• non-Lipschitz conditions
• adapted solutions
• pathwise uniqueness
• global solutions
• fixed point technique
• Schauder's fixed point theorem.

MSC

•  60H20
•  93E05

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