“…If a sufficiently regular solution of the system (1) exists then v i (s, x) is nothing else but the optimal profit that can be generated by switching, with initial conditions i for the system's mode and x for the process X at time s ∈ [0, T]. Probabilistic solution methods for optimal switching problems have been investigated since the 1970s and 1980s in various degrees of generality (see, for instance, [4], [26], [28], [34], and [35]), and most of the recent research in this area has been a combination of the martingale approach via Snell envelopes [11], [24], and the theory of backward stochastic differential equations (BSDE) [7], [14], [20].…”