Abstract
We study a finite horizon balance sheet optimal multi-modes switching problem related to trade-off strategies between expected profit and cost cash flows. The problem is formulated in terms of Snell envelopes for the profit and the cost yields which act as obstacles to each other, moreover we fully characterize the optimal strategies. Then using the link between the Snell envelope of processes and reflected backward stochastic differential equations (RBSDEs for short), solving the problem turns out actually to solving the related system of RBSDEs, for which we prove the existence of a continuous minimal solution using an approximation scheme.