  In this paper we obtain results for the existence and uniqueness of solutions
to coupled Forward-Backward Stochastic Differential Equations (FBSDEs) with
jumps defined on a random environment. This environment corresponds to a
measured-valued process, similar to the one found in Conditional McKean-Vlasov
Differential Equations and Mean-Field Games with Common Noise. The jump term in
the FBSDE is dependent on the environment through a stochastic intensity
process. We provide examples which relate our model with FBSDEs driven by Cox
and Hawkes processes, as well as regime-switching Conditional McKean-Vlasov
differential equations.
