Conditional Risk Mappings

Abstract

We introduce an axiomatic definition of a conditional convex risk mapping. By employing the techniques of conjugate duality we derive properties of conditional risk mappings. In particular, we prove a representation theorem for conditional risk mappings in terms of conditional expectations. We also develop dynamic programming relations for multistage optimization problems involving conditional risk mappings.Risk, Convex Analysis, Conjugate Duality, Stochastic Optimization, Dynamic Programming, Multi-Stage Programming