A converse comparison theorem for backward stochastic differential equations with jumps (Q625023)

Let \[ Y_t= \xi_T+ \int^T_t f(s,Y_s, Z_s, U_s)\,ds- \int^T_t Z_s dW_s- \int^T_t \int_B U_s(x) \widetilde\mu(ds, ds),\;0\leq t\leq T\tag{1} \] be backward stochastic differential equation with jumps. The author proves the converse comparison theorem for (1). Under certain assumptions, he shows that if for any \(r\), \(v\), \(0\leq r< v\leq T\) there exists a terminal condition \(\xi\), such that \[ \begin{aligned} Y_r(f_1,\xi_v)\leq Y_r(f_2, \xi_v)\quad & P\text{-a.s.}\qquad\text{then}\\ f_1(t,y,z,u)\leq f_2(t, y,z,u)\quad & P\text{-a.s.}.\end{aligned} \]