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August, 1993 Backward-Forward Stochastic Differential Equations
Fabio Antonelli
Ann. Appl. Probab. 3(3): 777-793 (August, 1993). DOI: 10.1214/aoap/1177005363

Abstract

This paper shows the existence and uniqueness of the solution of a backward stochastic differential equation inspired from a model for stochastic differential utility in finance theory. We show our results assuming, when possible, no more than the integrability of the terms involved in the equation. We also show the existence and uniqueness of the solution of a backward-forward stochastic differential equation, where the solution depends explicitly on both the past and the future of its own trajectory, under a more restrictive hypothesis on the Lipschitz constant.

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Fabio Antonelli. "Backward-Forward Stochastic Differential Equations." Ann. Appl. Probab. 3 (3) 777 - 793, August, 1993. https://doi.org/10.1214/aoap/1177005363

Information

Published: August, 1993
First available in Project Euclid: 19 April 2007

zbMATH: 0780.60058
MathSciNet: MR1233625
Digital Object Identifier: 10.1214/aoap/1177005363

Subjects:
Primary: 60H10
Secondary: 34F05

Keywords: Adapted process , backward-forward stochastic differential equations , semimartingale optional projection

Rights: Copyright © 1993 Institute of Mathematical Statistics

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Vol.3 • No. 3 • August, 1993
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