Speaker
Description
Let $(\Omega,\mathcal F,P)$ be a complete probability space and $\mathbb F:=(\mathcal F_t)$ be a filtration on $(\Omega,\mathcal F,P)$ satisfying usual conditions. Let $T>0$, $\nu$ be a natural number, and $\xi$ be an $\mathbb R^\nu$-valued $\mathcal F_T$-adapted random vector. We shall present the existence results for the following system of quadratic growth (with respect to $M$) backward SDEs of the form
\begin{equation}
Y^j_t=\xi^j+\int_t^TdF^j(s,Y,M)-\int_t^TdM^j_s,\quad j=1,\dots,\nu,
\end{equation}
where for any pair $(Y,M)\in \mathcal S^2_{\mathbb F}(0,T)\times \mathcal M^2_0(0,T)$ the mapping
\begin{equation}
[0,T]\ni s\longmapsto F^j(s,Y,M) \in \mathbb R
\end{equation}
is a finite variation continuous $\mathbb F$-adapted process with $F(0,Y,M)=0$. Then some application will be presented.
