A pathwise approach to backward and forward stochastic differential equations on the poisson space^*

Abstract

We study the existence and uniqueness of pathwise solutions to backward and forward stochastic differential equations on the Poisson space. We obtain the structure of these pathwise solutions to give the relationship between them. Also, in the bilinear case, we calculate the explicit form of their chaos decompositions.

^*Partially supported by DGICYT grant PB93-0052, PB96-1182 and CIRIT grant 97-SGR00144.

Acknowledgments

Part of this work was done while the first author was visiting Universitat Autònoma de Barcelona and Universitat de Barcelona. The authors express their thanks for the support of both centers.

Notes

^*Partially supported by DGICYT grant PB93-0052, PB96-1182 and CIRIT grant 97-SGR00144.