Journal of Applied Mathematics and Stochastic Analysis
Volume 13 (2000), Issue 3, Pages 207-238
BSDEs with polynomial growth generators
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.
AbstractIn 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.