Before revision:  The notion of effective scaling domain is introduced and its properties are discussed .
After revision:  It is then pointed out that such a relationship opens a door to a decomposition scheme, called progressive hedging, for solving multistage risk minimization and regret minimization problems. In particular, the classical progressive hedging algorithm is modified in order to handle a new class of constraints that arises from a reformulation of risk and regret minimization problems. Numerical results are provided to show the efficiency of the progressive hedging algorithms .