Conditional Risk Mappings

We introduce an axiomatic definition of a conditional convex risk mapping and we derive its properties. 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. Key words: Risk, Convex Analysis, Conjugate Duality, Stochastic Optimization, Dynamic Programming, Multi-stage Programming.

• Type: Journal
• Year: 2006
• Where: MOR
• Authors: Andrzej Ruszczynski, Alexander Shapiro
• Keywords: Conditional Convex Risk, Conditional Risk Mappings, MOR 2006, Risk Mappings