Stochastic dynamic programming (SDP) with a conditional value-at-risk (CVaR) criterion for management of storm-water

We present a new approach to stochastic dynamic programming (SDP) to determine a policy for management of urban storm-water that minimises conditional value-at-risk (CVaR). Storm-water flows into a large capture dam and is subsequently pumped to a holding dam. Water is then supplied directly to users or stored in an underground aquifer. We assume random inflow and constant demand. SDP is used to find a pumping policy that minimises CVaR, with a penalty for increased risk of environmental damage, and a pumping policy that maximises expected monetary value (EMV). We use both value iteration and policy improvement to show that the optimal policy under CVaR differs from the optimal policy under EMV.