Time-consistent approximations of risk-averse multistage stochastic optimization problems

In this paper we study the concept of time consistency as it relates to multistage risk-averse stochastic optimization problems on finite scenario trees. We use dynamic time-consistent formulations to approximate problems having a single coherent risk measure applied to the aggregated costs over all time periods. The dual representation of coherent risk measures is used to create a time-consistent cutting plane algorithm. Additionally, we also develop methods for the construction of universal time-consistent upper bounds, when the objective function is the mean-semideviation measure of risk. Our numerical results indicate that the resulting dynamic formulations yield close approximations to the original problem.