Al Ghanim, Dalal;
Loeffen, Ronnie;
Watson, Alexander R;
(2026)
Stochastic optimal control of Lévy tax processes with bailouts.
Insurance: Mathematics and Economics
10.1016/j.insmatheco.2026.103226.
(In press).
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Abstract
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.
| Type: | Article |
|---|---|
| Title: | Stochastic optimal control of Lévy tax processes with bailouts |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1016/j.insmatheco.2026.103226 |
| Publisher version: | https://doi.org/10.1016/j.insmatheco.2026.103226 |
| Language: | English |
| Additional information: | This is an Open Access article published under a Creative Commons Attribution 4.0 International (CC BY 4.0) Licence (https://creativecommons.org/licenses/by/4.0/). |
| Keywords: | Risk process, tax process, spectrally negative Lévy process, capital injections, optimal control, perturbed Lévy process, Skorokhod reflection |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10220637 |
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