A simple model on streamflow management with a dynamic risk measure

TL;DR

This paper introduces an exactly-solvable stochastic differential game model for flood management that uses a Levy process-driven streamflow and an entropic dynamic risk measure to optimize mitigation strategies under uncertainty.

Contribution

It provides a novel, explicit solution for flood risk minimization using a Hamilton-Jacobi-Bellman-Isaacs framework with model uncertainty considerations.

Findings

Explicit optimal flood mitigation policy derived

Existence criteria for the policy established

Worst-case probability measure identified

Abstract

We present an exactly-solvable risk-minimizing stochastic differential game for flood management in rivers. The streamflow dynamics follow stochastic differential equations driven by a Levy 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.