One-dimensional backward stochastic differential equations whose coefficient is monotonic in y and non-Lipschitz in z

Philippe Briand (1) , Jean-Pierre Lepeltier (2) , Jaime San Martin (3, 4, 3)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 LSP-EA3263 - Laboratoire de Statistique et Processus
3 CMM - Centre de modélisation mathématique / Centro de Modelamiento Matemático [Santiago]
4 DIM - Departamento de Ingeniería Matemática [Santiago]

In this paper we study one-dimensional BSDE's whose coefficient f is monotonic in y and non-Lipschitz in z. We obtain a general existence result when f has at most quadratic growth in z and is bounded. We study the special case f (t, y, z) = vertical bar z vertical bar(p) where p is an element of (1, 2]. Finally, we study the case f has a linear growth in z, general growth in y and is not necessarily bounded.

Mots clés: backward stochatic differential equations; monotonic non-Lipschitz coefficient

Domaines: Probabilités [math.PR]

Philippe Briand, Jean-Pierre Lepeltier, Jaime San Martin. One-dimensional backward stochastic differential equations whose coefficient is monotonic in y and non-Lipschitz in z. Bernoulli, 2007, 13 (1), pp.80-91. ⟨10.3150/07-BEJ5004⟩. ⟨hal-00364645⟩