Dynamic programming with non-convex risk-sensitive measures

Dynamic programming with risk-sensitive performance criteria has applications in many fields (e.g., operations research, finance, control systems). Historically, risk-sensitive performance criteria have been represented using expected utility functions. More recently, literature on dynamic performance (i.e., risk or reward) measures has inspired an alternative approach to risk-sensitive performance evaluation. The dynamic performance measure approach is a generalization of the classical work using expected value. One drawback of this approach is that it has only been developed with convex/coherent performance measures, which exclude a large class of important non-convex performance criteria (e.g., Cumulative Prospect Theory (CPT)). We remedy this drawback by proving the existence of dynamic programming equations for non-convex performance criteria.