Optimal multi-dimensional stochastic harvesting with density-dependent prices

2014/06/30 by Luis H. R. Alvarez, Alvarez, Luis H. R., Edward Lungu +3
Mathematics · #92D25 #93E20 #FOS: Mathematics #Optimization and Control (math.OC) #Primary 60H10 #Secondary 91B70 #math.OC #msc:60H10 #msc:91B70 #msc:92D25 #msc:93E20

paper · pdf · doi:10.48550/arxiv.1406.7668

arxiv created 2015/06/26 · arxiv updated 2015/06/29

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 Δx and Δt go to 0 of taking out a sequence of small quantities of size Δx within small time periods of size Δt.

Related

• Harvesting of a stochastic population under a mixed regular-singular control formulation
• Singular mean-field control games with applications to optimal harvesting and investment problems
• On an Optimal Extraction Problem with Regime Switching
• Optimal Policy Characterization for a Class of Multi-Dimensional Ergodic Singular Stochastic Control Problems
• Optimal dividends with partial information and stopping of a degenerate\n reflecting diffusion