Dynamic programming for discrete-time finite horizon optimal switching   problems with negative switching costs
  This paper studies a discrete-time optimal switching problem on a finite horizon. The underlying model has a running reward, terminal reward and signed (positive and negative) switching costs. Using the martingale approach to optimal stopping problems, we extend a well known explicit dynamic programming method for computing the value function and the optimal strategy to the case of signed switching costs. 
Randall Martyr
math.OC math.PR