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Harvesting of interacting stochastic populations. (arXiv:1810.05609v1 [math.PR])
来源于:arXiv
We analyze the optimal harvesting problem for an ecosystem of species that
experience environmental stochasticity. Our work generalizes the current
literature significantly by taking into account non-linear interactions between
species, state-dependent prices, and species injections. The key generalization
is making it possible to not only harvest, but also `seed' individuals into the
ecosystem. This is motivated by how fisheries and certain endangered species
are controlled. The harvesting problem becomes finding the optimal
harvesting-seeding strategy that maximizes the expected total income from the
harvest minus the lost income from the species injections. Our analysis shows
that new phenomena emerge due to the possibility of species injections.
It is well-known that multidimensional harvesting problems are very hard to
tackle. We are able to make progress, by characterizing the value function as a
viscosity solution of the associated Hamilton-Jacobi-Bellman (HJB) equations.
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