Optimal harvesting strategies for stochastic ecosystems

Focusing on multidimensional stochastic Lotka-Volterra type ecosystems in which multiple species are interacting, this study aims developing optimal harvesting strategies. The underlying systems are controlled regime-switching diffusions. Dealing with such a class of singular controls, the authors' objective is to maximise the total expected discounted rewards by using the ideas from singular control theory. In this study, the finiteness of the value function is obtained. The value function is characterised as a viscosity solution of the associated coupled systems of quasi-variational inequalities. Chattering policies are developed, which provide candidates for lower bounds of value functions. The impact of large noise on harvesting is studied by using certain upper bounds.