Two-stage stochastic optimization problems with stochastic ordering constraints on the recourse

We consider two-stage risk-averse stochastic optimization problems with a stochastic ordering constraint on the recourse function. Two new characterizations of the increasing convex order relation are provided. They are based on conditional expectations and on integrated quantile functions: a counterpart of the Lorenz function. We propose two decomposition methods to solve the problems and prove their convergence. Our methods exploit the decomposition structure of the risk-neutral two-stage problems and construct successive approximations of the stochastic ordering constraints. Numerical results confirm the efficiency of the methods.

► Two-stage problems with order-constraint on the recourse are analyzed.
► Increasing convex order (ICO) is consistent with risk-averse preferences.
► Increasing convex order can be defined by conditional expectations. ICO can be expressed by a counterpart of the Lorenz function using upper quantiles.
► Two decomposition methods with finite convergence are proposed.