Optimal multi-dimensional stochastic harvesting with density-dependent prices

被引：7

作者：

Alvarez L.H.R. ^{[1
]}

Lungu E. ^{[2
]}

Øksendal B. ^{[3
,4
]}

机构：

[1] Department of Accounting and Finance, Turku School of Economics, University of Turku, Turku

[2] Department of Mathematics, University of Botswana, B.P. 0022, Gaborone

[3] Department of Mathematics, University of Oslo, Box 1053, Blindern, Oslo

[4] Norwegian School of Economics, Helleveien 30, Bergen

来源：

Afrika Matematika | 2016年 / 27卷 / 3-4期

基金：

欧洲研究理事会;

关键词：

Chattering policies; Density-dependent prices; Interacting populations; Itô; diffusions; Optimal harvesting; Singular stochastic control; Verification theorem;

D O I：

10.1007/s13370-015-0357-0

中图分类号：

学科分类号：

摘要：

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. © 2015, African Mathematical Union and Springer-Verlag Berlin Heidelberg.

引用

页码：427 / 442

页数：15

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