Risk-averse multistage stochastic programs with expected conditional risk measures

We study risk-averse multistage stochastic programs with expected conditional risk measures (ECRMs). ECRMs are attractive because they are time-consistent, which means that a plan made today will not be changed in the future if the problem is re-solved given a realization of the random variables. We show that the computational burden of solving the risk-averse problems based on ECRMs is the same as the risk-neutral ones. We consider ECRMs for both quantile and deviation mean-risk measures, deriving the Bellman equations in each case. Finally, we illustrate our results with extensive numerical computations for problems from two applications: hydrothermal scheduling and portfolio selection. The results show that the ECRM approach provides higher expected costs in the early stages to hedge against cost spikes in later stages for the hydrothermal scheduling problem. For the portfolio selection problem, the new approach gives well-diversified portfolios over time. Overall, the ECRM approach provides superior performance over the risk-neutral model under extreme scenario conditions.