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Harvesting a renewable resource under uncertainty. (English) Zbl 1179.91205
Summary: This paper presents a theory of harvesting that allows for partial harvests and accounts for the risk of extinction, for biological assets with size-dependent stochastic growth. The harvesting decision is formulated as a disinvestment problem in continuous time and generalized Faustmann formulas are derived. The probability of extinction is then analyzed for a wide class of growth functions. An illustration based on the logistic Brownian motion shows that both optimal biomass at harvest and harvest size do not vary monotonically with uncertainty. More generally, this paper illustrates the importance of properly accounting for barriers in stochastic investment problems.

MSC:
91B76 Environmental economics (natural resource models, harvesting, pollution, etc.)
91B70 Stochastic models in economics
91B62 Economic growth models
91G50 Corporate finance (dividends, real options, etc.)
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