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Optimal harvesting for a stochastic regime-switching logistic diffusion system with jumps
Affiliation:1. Department of Mathematics, Harbin Institute of Technology (Weihai), Weihai 264209, PR China;2. School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, PR China;1. Department of Electrical Engineering, College of Engineering, Tehran Science and Research Branch, Islamic Azad University, Tehran, Iran;2. Complex Systems Research Laboratory, Iran University of Science and Technology, Tehran, Iran;3. Electrical Engineering Department, Shahid Bahonar University of Kerman, Iran;1. College of Electrical and Information Engineering, Southwest University for Nationalities of China, Chengdu, Sichuan, 610041, China;2. Department of Mechanical Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong;1. College of Management and Economics, Tianjin University, Tianjin 300072, China;2. School of International Trade and Economics, University of International Business and Economics, Beijing 100029, China;3. School of Statistics, University of International Business and Economics, Beijing 100029, China;1. Department of Electrical Engineering, National Tsing Hua University, Hsinchu 30013, Taiwan;2. Department of Electrical Engineering, Hsiuping University of Science and Technology, Taichung 41280, Taiwan;3. College of Information and Electrical Engineering, Shandong University of Science and Technology, Qingdao 266510, PR China
Abstract:The optimization problem of fishing for a stochastic logistic model is studied in this paper. Besides a standard geometric Brownian motion, another two driving processes are taken into account: a stationary Poisson point process and a continuous-time finite-state Markov chain. The classical harvesting problem for this model is a big difficult puzzle since the corresponding Fokker–Planck equations with three types of noise are very difficult to solve. Our main goal of this paper is to work out the optimization problem with respect to stationary probability density. One of the main contributions is to provide a new equivalent approach to overcome this problem. More precisely, an ergodic method is used to show the almost surely equivalency between the time averaging yield and sustainable yield. Results show that the optimal strategy changes with environment. An interesting thing is that the optimal strategy for each state is equivalent to the global optimality.
Keywords:Optimal harvesting strategy  Maximum yield  Jumping noise  Asymptotically stable in distribution  Ergodic method
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