Power identities for L\'evy risk models under taxation and capital injections
Abstract
In this paper we study a spectrally negative L\'evy process which is refracted at its running maximum and at the same time reflected from below at a certain level. Such a process can for instance be used to model an insurance surplus process subject to tax payments according to a loss-carry-forward scheme together with the flow of minimal capital injections required to keep the surplus process non-negative. We characterize the first passage time over an arbitrary level and the cumulative amount of injected capital up to this time by their joint Laplace transform, and show that it satisfies a simple power relation to the case without refraction. It turns out that this identity can also be extended to a certain type of refraction from below. The net present value of tax collected before the cumulative injected capital exceeds a certain amount is determined, and a numerical illustration is provided.
Keywords
Cite
@article{arxiv.1310.3052,
title = {Power identities for L\'evy risk models under taxation and capital injections},
author = {Hansjoerg Albrecher and Jevgenijs Ivanovs},
journal= {arXiv preprint arXiv:1310.3052},
year = {2014}
}