A Simple Model on Streamflow Management with a Dynamic Risk Measure

Abstract

AbstractWe present an exactly solvable risk-minimizing stochastic differential game for flood management in rivers for sustainable and adaptive water management. The streamflow dynamics follow stochastic differential equations driven by a Lévy process. An entropic dynamic risk measure is employed to evaluate a flood risk under model uncertainty. The problem is solved via a Hamilton–Jacobi–Bellman–Isaacs equation. We explicitly derive an optimal flood mitigation policy along with its existence criteria and the worst-case probability measure. A backward stochastic differential representation as an alternative formulation is also presented. Our contribution provides a new mathematical approach for better understanding water management.KeywordsRiver management under uncertaintyLévy processZero-sum differential gameHamilton-Jacobi-Bellman-Isaacs equation