A simple model on streamflow management with a dynamic risk measure

2020/10/29 by Hidekazu Yoshioka, Yoshioka, Hidekazu, Yumi Yoshioka +1
Decision Sciences · Engineering · Environmental Science · #FOS: Mathematics #Flood Risk Assessment and Management #Optimization and Control (math.OC) #Probability (math.PR) #Risk and Portfolio Optimization #Water resources management and optimization

paper · pdf · doi:10.48550/arxiv.2010.15290

openalex publication_date 2020/10/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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