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Optimal multi-dimensional stochastic harvesting with density-dependent prices

Alvarez, Luis H.; Lungu, Edward; Øksendal, Bernt
Journal article, Peer reviewed
Accepted version
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URI
http://hdl.handle.net/11250/2466585
Date
2016
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  • Publikasjoner fra CRIStin (NHH) [243]
Original version
Afrika Matematika. 2016, 27 (3), 427-442.   10.1007/s13370-015-0357-0
Abstract
We prove a verification theorem for a class of singular control problems which model

optimal harvesting with density-dependent prices or optimal dividend policy with capitaldependent

utilities. The result is applied to solve explicitly some examples of such optimal

harvesting/optimal dividend problems.

In particular, we show that if the unit price decreases with population density, then the

optimal harvesting policy may not exist in the ordinary sense, but can be expressed as a

”chattering policy”, i.e. the limit as ∆x and ∆t go to 0 of taking out a sequence of small

quantities of size ∆x within small time periods of size ∆t.
Journal
Afrika Matematika

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