10 research outputs found
General Existence Results for Reflected BSDE and BSDE
In this paper, we are concerned with the problem of existence of solutions
for generalized reflected backward stochastic differential equations (GRBSDEs
for short) and generalized backward stochastic differential equations (GBSDEs
for short) when the generator is continuous with general growth
with respect to the variable and stochastic quadratic growth with respect
to the variable . We deal with the case of a bounded terminal condition
and a bounded barrier as well as the case of unbounded ones. This is
done by using the notion of generalized BSDEs with two reflecting barriers
studied in \cite{EH}. The work is suggested by the interest the results might
have in finance, control and game theory.Comment: 23 page
Doubly Reflected BSDEs With Stochastic Quadratic Growth: Around The Predictable Obstacles
We prove the existence of maximal (and minimal) solution for one-dimensional
generalized doubly reflected backward stochastic differential equation (RBSDE
for short) with irregular barriers and stochastic quadratic growth, for which
the solution has to remain between two rcll barriers and on , and its left limit has to stay respectively above and below two
predictable barriers and on . This is done without assuming any
-integrability conditions and under weaker assumptions on the input data. In
particular, we construct a maximal solution for such a RBSDE when the terminal
condition is only measurable and the driver is
continuous with general growth with respect to the variable and stochastic
quadratic growth with respect to the variable . Our result is based on a
(generalized) penalization method. This method allow us find an equivalent form
to our original RBSDE where its solution has to remain between two new rcll
reflecting barriers and which are, roughly
speaking, the limit of the penalizing equations driven by the dominating
conditions assumed on the coefficients. A standard and equivalent form to our
initial RBSDE as well as a characterization of the solution as a
generalized Snell envelope of some given predictable process are also
given.Comment: 21 page
Reflected Backward Stochastic Differential Equation with Jumps and RCLL Obstacle
In this paper we study one-dimensional reflected backward stochastic differential equation when the noise is driven by a Brownian motion and an independent Poisson point process when the solution is forced to stay above a right continuous left-hand limited obstacle. We prove existence and uniqueness of the solution by using a penalization method combined with a monotonic limit theorem
Large deviation for BSDE with subdifferential operator
In this paper we prove that the solution of a backward stochastic differential equation, which involves a subdifferential operator and associated to a family of reflecting diffusion processes, converges to the solution of a deterministic backward equation and satisfes a large deviation principle