  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.
