“…Motivated by the analysis of mathematical models of the CO 2 emissions markets, see for example [3,18,2,4, 1], we are interested in the case of forward processes (X t = (P t , E t )) 0≤t≤T having a onedimensional component (E t ) 0≤t≤T with bounded variations, and a backward component (Y t ) 0≤t≤T having a terminal value given by a monotone function φ of E T , and especially when φ is an indicator function of the form φ = 1 [Λ,+∞) . In [1], we proposed an unrealistic toy example for which we showed that, while the terminal condition could not be enforced, it was still possible to prove existence and uniqueness of a solution provided parts of the terminal condition are allowed to become part of the solution.…”