Backward stochastic differential equations with jumps involving a subdifferential operator (Q2722265)

A reflected backward stochastic differential equation (BSDE) of the Wiener-Poisson type associated to a multivalued maximal monotone operator on \({\mathbb R}^{d}\) is defined by the subdifferential of a convex function \(F\). This is the continuation of the previous work by \textit{Y. Ouknine} [Stochastics Stochastics Rep. 65, No. 1-2, 111-125 (1998; Zbl 0918.60046)]. This kind of problem has been studied by many authors in the case of stochastic ordinary differential equations. Existence and uniqueness of the solution by Yosida approximation via penalization approach are proved. This approach is given in the one-dimensional case by \textit{Y. Ouknine} (loc. cit.). The reflecting process is shown to be absolutely continuous. A new class of singular BSDE which can be solved by using these results is given. The paper is closed by studying Malliavin derivative of the solution and to establish the link between the solution of the BSDE and the process \(Z\) which is very important in mathematical finance.