Optimal Control of Fisheries under Regime Switching and in MPAs

• Applicant: Privatdozent Dr. Thorsten Upmann
• Subject Area: Economic Theory
• Term: since 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 542390673

The project aims at advancing inter-temporal modelling of marine renewable natural resources—fish— and to derive optimal policies for their sustainable management, addressing two critical issues: development of management strategies in the presence of thresholds that may lead to regime switching in the stock dynamics (work package RSW) and the optimal design of marine protected areas (MPAs) to protect fish stocks and their habitat (work package MPA). To deal with these problems, we apply the theory of optimal control (OC), namely hybrid OC in the management of regime switching and distributed OC in the design of MPAs. To enhance realism of our approach, the specified models will be calibrated to European data on fish stocks and fisheries, which will be provided by the B-USEFUL in 2024. The project is complemented by mutual contributions of the partners in the Package Proposal/Antragspaket. Work package RSW focuses on management of fish stocks in the neighbourhood of the switching manifold where the system dynamics undergo an abrupt change or regime shift. This opens the scope for two types of specific policies: sliding behaviour, where the policies keep the system between both regimes for some time; and hybrid limit cycles, where policies induce cycling behaviour that repeatedly transgresses the switching boundary back and forth. Furthermore, the project considers the effects of parametric uncertainty, where the occurrence of a regime shift may be driven by a stochastic event. To explore the effects of this type of uncertainty on fishing management and the incentives to acquire additional information, the project uses the concept of value of information (VoI). Work package MPA focuses on the optimal design of MPAs in terms of their size, location and shape to protect fish stocks and their habitat. The study formulates a spatio-temporal fishery model that incorporates the spatial distribution and movement of fish, fishing activities, fishing capacity constraints, adverse effects of fishing on the habitat, and the spatial dimensions and configuration of MPAs. By taking these features into account, the model is enhanced in its realism and policy relevance while still being mathematically tractable. The planning problem of an MPA already presents a considerable level of intricacy due to the state dynamics being governed by a coupled reaction-diffusion partial differential equation system. It becomes even more challenging when we next consider the adverse impact of fishing on the habitat and explicitly take into account the habitat’s dynamics. Both work packages, RSW and MPA, focus on the inter-temporal modelling of fish stocks, and seek to develop optimal policies for their sustainable management when the stock dynamics are subject to switches either at specific stock levels or at specific locations. Overall, the project aims to provide valuable insights and policy conclusions for sustainable management and conservation of marine resources.

• DFG Programme: Research Grants