20 February 2014

16:00

to

17:30

Ying Hu

Abstract

In this work, we want to construct the solution $(Y,Z,K)$ to the following BSDE
$$\begin{array}{l}
Y_t=\xi+\int_t^Tf(s,Y_s,Z_s)ds-\int_t^TZ_sdB_s+K_T-K_t, \quad 0\le t\le T, \\
{\mathbf E}[l(t, Y_t)]\ge 0, \quad 0\le t\le T,\\
\int_0^T{\mathbf E}[l(t, Y_t)]dK_t=0, \\
\end{array}
$$
where $x\mapsto l(t, x)$ is non-decreasing and the terminal condition $\xi$
is such that ${\mathbf E}[l(T,\xi)]\ge 0$.
This equation is different from the (classical) reflected BSDE. In particular, for a solution $(Y,Z,K)$,
we require that $K$ is deterministic. We will first study the case when $l$ is linear, and then general cases.
We also give some application to mathematical finance. This is a joint work with Philippe Briand and Romuald Elie.