Abstract
We 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.
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Kurita Water and Environment Foundation 19B018 and 20K004 support this research.
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Yoshioka, H., Yoshioka, Y. (2022). A Simple Model on Streamflow Management with a Dynamic Risk Measure. In: Giri, D., Raymond Choo, KK., Ponnusamy, S., Meng, W., Akleylek, S., Prasad Maity, S. (eds) Proceedings of the Seventh International Conference on Mathematics and Computing . Advances in Intelligent Systems and Computing, vol 1412. Springer, Singapore. https://doi.org/10.1007/978-981-16-6890-6_71
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DOI: https://doi.org/10.1007/978-981-16-6890-6_71
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