Dynamic sampling algorithms for multi-stage stochastic programs with risk aversion

We consider the incorporation of a time-consistent coherent risk measure into a multi-stage stochastic programming model, so that the model can be solved using a SDDP-type algorithm. We describe the implementation of this algorithm, and study the solutions it gives for an application of hydro-thermal scheduling in the New Zealand electricity system. The performance of policies using this risk measure at different levels of risk aversion is compared with the risk-neutral policy.

► A risk averse objective is modelled in a multi-stage stochastic program.
► The risk measure is coherent and time-consistent.
► Large scale instances can be solved by sampling in an SDDP-type algorithm.
► The model is effective at reducing risk of a hydro-thermal electricity system.
► The model can eliminate the effects of bad outcomes at a modest cost increase.