2019/09/23 by Sören Christensen, Christensen, Sören, Tobias Sohr +1
Business, Management and Accounting · Mathematics · #49N25 #60G40 #60G51 #90B05 #93E20 #Advanced Queuing Theory Analysis #FOS: Mathematics #Nonlinear Differential Equations Analysis #Probability (math.PR) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1909.10182
openalex publication_date 2019/09/23 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28
This article treats long term average impulse control problems with running\ncosts in the case that the underlying process is a L 'evy process. Under quite\ngeneral conditions we characterize the value of the control problem as the\nvalue of a stopping problem and construct an optimal strategy of the control\nproblem out of an optimizer of the stopping problem if the latter exists.\nAssuming a maximum representation for the payoff function, we give easy to\nverify conditions for the control problem to have an \(s,S\)\nstrategy as an optimizer. The occurring thresholds are given by the roots of an\nexplicit auxiliary function. This leads to a step by step solution technique\nwhose utility we demonstrate by solving a variety of examples of impulse\ncontrol problems.\n