Optimal multi-dimensional stochastic harvesting with density-dependent prices

Journal article

Authors / Editors

Lungu, Edward

Research Areas

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Publication Details

Author list: Alvarez LHR, Lungu E, Oksendal B

Publisher: Springer

Place: HEIDELBERG

Publication year: 2016

Journal: Afrika Matematica (1012-9405)

Journal acronym: AFR MAT

Volume number: 27

Issue number: 3-4

Start page: 427

End page: 442

Number of pages: 16

ISSN: 1012-9405

eISSN: 2190-7668

Languages: English-Great Britain (EN-GB)

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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 capital-dependent 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 Delta x and Delta t go to 0 of taking out a sequence of small quantities of size Delta x within small time periods of size Delta t.

Keywords

Chattering policies, Density-dependent prices, Interacting populations, Ito diffusions, optimal harvesting, singular stochastic control, verification theorem

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