Quadratic two-stage stochastic optimization with coherent measures of risk

A new scheme to cope with two-stage stochastic optimization problems uses a risk measure as the objective function of the recourse action, where the risk measure is defined as the worst-case expected values over a set of constrained distributions. This paper develops an approach to deal with the case where both the first and second stage objective functions are convex linearquadratic. It is shown that under a standard set of regularity assumptions, this two-stage quadratic stochastic optimization problem with measures of risk is equivalent to a conic optimization problem that can be solved in polynomial time.