Sergiu Ungureanu
City, University of London, London, UK

We consider the problem of harvesting from a stochastic population while avoiding extinction. Using ergodic optimal control, we find the optimal harvesting strategy which maximizes the asymptotic yield of harvested individuals. When the benefit is linear in the harvested amount, we find that a bang-bang strategy is optimal under very general conditions. The effects of parameter changes are explored.

More realistic environments have very complex stochasticity. On top of the usual white-noise environmental variation, there can be seasonal variation, and the environment can suffer from large but random changes. It is likely impossible to explicitly solve complex models with many layers of stochasticity, but numerical methods can help and therefore the models are useful. We find theoretical results that justify the use of the Markov chain approximation method, developed by Kushner & Martins (1991) and Kushner & Dupuis (1992), in finding numerical approximations of the optimal strategies and value functions in a very large class of models. These models can have general cost functions of harvesting or seeding, price functions reactive to market conditions and random fluctuations, seasonal fluctuations, and large-scale random fluctuations. The numerical methods are used to explore for interesting intuitions and unusual findings, which would not have been available theoretically.