Optimal multi-dimensional stochastic harvesting with density-dependent prices

Luis H.R. Alvarez, Edward Lungu, Bernt Øksendal

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


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 Δ x and Δ t go to 0 of taking out a sequence of small quantities of size Δ x within small time periods of size Δ t.

Original languageEnglish
Pages (from-to)427-442
Number of pages16
JournalAfrika Matematika
Issue number3-4
Publication statusPublished - Jun 1 2016

All Science Journal Classification (ASJC) codes

  • General Mathematics


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