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Fixed point technique for a large class of backward stochastic differential equations
by
R. Negrea
Universitatea Politehnica din Timisoara, Dapartamentul de Matematica
Coauthors: L.Cadariu
In the frame of the stochastic differential equations (SDE) there exists an important difference from the classical (non-stochastic or deterministic) frame: a solution is a stochastic process which satisfies identically the equation and has some common properties, but, it must to be Ft-measurable for any 0 < t < 1.These last properties make a difference between forward and backward stochastic differential equation (BSDE): in the forward stochastic frame the Ft-measurability is assured using the natural filtration generated by the (Xs; 0 < s < t), but in the backward stochastic case (i.e. an equation with a final condition) a natural filtration cannot be obtained, so a solution made using the successive approximation method not assure the property of the measurability. Therefore, the existence of a solution for a BSDE can be proved using some alternative methods as for example the technique of fixed point theorem. In this paper we prove the existence of the solution for a BSDE combining the fixed point technique for some generalized contractions with the theory of stochastic operators.
Date received: March 29, 2008
Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cawh-18.