Risk-Averse Two-Stage Stochastic Linear Programming: Modeling and Decomposition

We formulate a risk-averse two-stage stochastic linear programming problem in which unresolved uncertainty remains after the second stage. The objective function is formulated as a composition of conditional risk measures. We analyze properties of the problem and derive necessary and sufficient optimality conditions. Next, we construct a new decomposition method for solving the problem that exploits the composite structure of the objective function. We illustrate its performance on a portfolio optimization problem.