Risk minimization, regret minimization and progressive hedging algorithms

摘要

Optimization models based on coherent regret measures and coherent riskmeasures are of essential importance in financial management and reliabilityengineering. This paper studies the dual representations of these two measures.The relationship between risk envelopes and regret envelopes are established byusing the Lagrangian duality theory. The notion of effective scaling domain isintroduced and its properties are discussed.