Journal of Applied Mathematics and Stochastic Analysis
Volume 13 (2000), Issue 3, Pages 207-238

BSDEs with polynomial growth generators

Philippe Briand1 and René Carmona2

1Université Rennes 1, IRMAR, Rennes Cedex 35 042, France
2Princeton University, Statistics & Operations Research, Princeton, NJ 08544, USA

Received 1 July 1998; Revised 1 July 1999

Copyright © 2000 Philippe Briand and René Carmona. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this paper, we give existence and uniqueness results for backward stochastic differential equations when the generator has a polynomial growth in the state variable. We deal with the case of a fixed terminal time, as well as the case of random terminal time. The need for this type of extension of the classical existence and uniqueness results comes from the desire to provide a probabilistic representation of the solutions of semilinear partial differential equations in the spirit of a nonlinear Feynman-Kac formula. Indeed, in many applications of interest, the nonlinearity is polynomial, e.g, the Allen-Cahn equation or the standard nonlinear heat and Schrödinger equations.