The Annals of Applied Probability

Backward-Forward Stochastic Differential Equations

Fabio Antonelli

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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.

Article information

Source
Ann. Appl. Probab., Volume 3, Number 3 (1993), 777-793.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1177005363

Digital Object Identifier
doi:10.1214/aoap/1177005363

Mathematical Reviews number (MathSciNet)
MR1233625

Zentralblatt MATH identifier
0780.60058

JSTOR
links.jstor.org

Subjects
Primary: 60H10: Stochastic ordinary differential equations [See also 34F05]
Secondary: 34F05: Equations and systems with randomness [See also 34K50, 60H10, 93E03]

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

Citation

Antonelli, Fabio. Backward-Forward Stochastic Differential Equations. Ann. Appl. Probab. 3 (1993), no. 3, 777--793. doi:10.1214/aoap/1177005363. https://projecteuclid.org/euclid.aoap/1177005363


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