Stochastic control of single-species population dynamics model subject to jump ambiguity

• Published in: Journal of biological dynamics Vol. 14; no. 1; pp. 696 - 729
• Main Authors: Yoshioka, Hidekazu, Tsujimura, Motoh
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 01.01.2020; Taylor & Francis Ltd; Taylor & Francis Group
• Subjects: Algae; algae bloom; Hamilton-Jacobi-Bellman-Isaacs equation; jump ambiguity; non-linearity and non-locality; Population dynamics; Viscosity
• ISSN: 1751-3758; 1751-3766; 1751-3766
• DOI: 10.1080/17513758.2020.1811408

A logistic type stochastic control model for cost-effective single-species population management subject to an ambiguous jump intensity is presented based on the modern multiplier-robust formulation. The Hamilton-Jacobi-Bellman-Isaacs (HJBI) equation for finding the optimal control is then derived. Mathematical analysis of the HJBI equation from the viewpoint of viscosity solutions is carried out with an emphasis on the non-linear and non-local term, which is a key term arising due to the jump ambiguity. We show that this term can be efficiently handled in the framework of viscosity solutions by utilizing its monotonicity property. A numerical scheme to discretize the HJBI equation is presented as well. Our model is finally applied to management of algae population in river environment. Optimal management policies ranging from the short-term to long-term viewpoints are numerically investigated.