Admissibility of additive jump coefficients in the m<n regime

Establish a different structural condition under which additive jump coefficients of the form h=h(t,x,e), with no U-feedback, are admissible for fully coupled McKean–Vlasov forward–backward stochastic differential equations with jumps when the backward dimension m is smaller than the forward dimension n.

Background

The paper’s monotonicity assumption imposes strict U-dissipativity when m<n: setting the differences in X, Y, and Z to zero shows that the jump coefficient must control arbitrary differences in the L²-valued jump integrand U. An additive jump coefficient h=h(t,x,e) has no U-feedback, so it cannot satisfy the stated monotonicity condition in the m<n rank regime. The authors identify the recovery of such additive coefficients under an alternative structural condition as unresolved.