Smooth solutions to discounted reward control problems with unbounded   discount rate and financial applications
  We consider a discounted reward control problem in continuous time stochastic environment where the discount rate might be an unbounded function of the control process. We provide a set of general assumptions to ensure that there exists a smooth classical solution to the corresponding HJB equation. Moreover, some verification reasoning are provided and the possible extension to dynamic games is discussed. At the end of the paper consumption - investment problems arising in financial economics are considered. 
Dariusz Zawisza
math.PR math.OC q-fin.MF