BSDEs with polynomial growth generators

By P. Briand, René A. Carmona. 2000

96 citations recorded by the source corpus.

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 Schrodinger equations.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/cb32c4973c14767f6c5ee93bd923cab3a339b14c

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Economics and Econometrics

1. Said Hamadène
2. Ying Hu
3. Anis Matoussi
4. Bernard Delyon
5. P. Briand
6. Shige Peng

In Finance

1. Said Hamadène
2. P. Briand
3. Alexandre Popier
4. Mingyu Xu
5. Ying Hu
6. Anis Matoussi
7. Shige Peng
8. Thomas Kruse

Citations in the corpus

• Reflected backward stochastic differential equations under monotonicity and general increasing growth conditions (2005, background): “More recently, Briand and Carmona (2000), Pardoux (1999), and Briand et al. (2003) studied the solution of a BSDE with a coefficient f (t, ω, y, z) that satisfies only monotonicity, continuity, and general increasing growth conditions with respect to y, and a Lipschitz condition on z.”
• Multidimensional backward stochastic differential equations with uniformly continuous coefficients (2003, background): “The improvements are not concerned with the regularity of f in z since it is usually supposed that f is Lipschitz with respect to that component (Pardoux 1999; Darling and Pardoux 1997; Briand and Carmona 2000; Mao 1995).”
• BSDEs with monotone generator driven by Brownian and Poisson noises in a general filtration (2014, background): “For example, Briand and Carmona [4] and Pardoux [31] consider the case of a monotonic generator w.”
• Lp solutions of backward stochastic differential equations (2003, background): “Briand et al. / Stochastic Processes and their Applications 108 (2003) 109–129”