Stochastic optimal control of Lévy tax processes with bailouts
研究如何通过税收和纾困两种手段控制一个光谱负莱维过程，求解最大化税收与纾困成本之差的期望现值的随机最优控制问题，扩展了控制类别并推广了扰动布朗运动的结果。
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.