A Full Balance Sheet Two-modes Optimal Switching problem

We formulate and solve a finite horizon full balance sheet two-modes optimal switching problem related to trade-off strategies between expected profit and cost yields. Given the current mode, this model allows for either a switch to the other mode or termination of the project, and this happens for both sides of the balance sheet. A novelty in this model is that the related obstacles are nonlinear in the underlying yields, whereas, they are linear in the standard optimal switching problem. The optimal switching problem is formulated in terms of a system of Snell envelopes for the profit and cost yields which act as obstacles to each other. We prove existence of a continuous minimal solution of this system using an approximation scheme and fully characterize the optimal switching strategy.