REFLECTED BSDE WITH SUPERLINEAR QUADRATIC COEFFICIENT
M. Kobylanski
J. P. Lepeltier
M. C. Quenez
S. Torres
Abstract: In this paper, we provide existence of a reflected solution of the one-dimensional
backward stochastic differential equation when the coefficient is continuous, has a superlinear
growth in 
and quadratic growth in 
We also give a characterization of the solution as
the value function of an optimal stopping time problem. We also study the links between the
solution of the quadratic RBSDE and the corresponding obstacle problem. Then we give an
application of quadratic RBSDE’s to the pricing of American contingent claims in an
incomplete market.
1991 AMS Mathematics Subject Classification: Primary -; Secondary -;
Key words and phrases: Backward stochastic differential equations, reflexion, viscosity
solution, American option.
