2014/08/05 by Erik J. Baurdoux, Baurdoux, Erik J., Kazutoshi Yamazaki +1 · 2 citations
Business, Management and Accounting · Decision Sciences · Economics, Econometrics and Finance · #49J40 #60G51 #93E20 #Advanced Queuing Theory Analysis #FOS: Mathematics #Optimization and Control (math.OC) #Probability (math.PR) #Probability and Risk Models #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1408.0847
openalex publication_date 2014/08/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a class of two-sided singular control problems. A controller either increases or decreases a given spectrally negative Levy process so as to minimize the total costs comprising of the running and control costs where the latter is proportional to the size of control. We provide a sufficient condition for the optimality of a double barrier strategy, and in particular show that it holds when the running cost function is convex. Using the fluctuation theory of doubly reflected Levy processes, we express concisely the optimal strategy as well as the value function using the scale function. Numerical examples are provided to confirm the analytical results.