2024/08/29 by Dalal Al Ghanim, Ghanim, Dalal Al, Ronnie Loeffen +3
Business, Management and Accounting · Economics, Econometrics and Finance · #Corporate Taxation and Avoidance #FOS: Mathematics #Fiscal Policies and Political Economy #Fiscal Policy and Economic Growth #Optimization and Control (math.OC) #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.2408.16385
openalex publication_date 2024/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider controlling the paths of a spectrally negative Lévy process by two means: the subtraction of `taxes' when the process is at an all-time maximum, and the addition of `bailouts' which keep the value of the process above zero. We solve the corresponding stochastic optimal control problem of maximising the expected present value of the difference between taxes received and cost of bailouts given. Our class of taxation controls is larger than has been considered up till now in the literature and makes the problem truly two-dimensional rather than one-dimensional. Along the way, we define and characterise a large class of controlled Lévy processes to which the optimal solution belongs, which extends a known result for perturbed Brownian motions to the case of a general Lévy process with no positive jumps.