The equivalence of two tax processes

Dalal Al Ghanim, Ronnie Loeffen and Alexander R. Watson

Insurance: Mathematics and Economics, 2020, vol. 90, issue C, 1-6

Abstract: We introduce two models of taxation, the latent and natural tax processes, which have both been used to represent loss-carry-forward taxation on the capital of an insurance company. In the natural tax process, the tax rate is a function of the current level of capital, whereas in the latent tax process, the tax rate is a function of the capital that would have resulted if no tax had been paid. Whereas up to now these two types of tax processes have been treated separately, we show that, in fact, they are essentially equivalent. This allows a unified treatment, translating results from one model to the other. Significantly, we solve the question of existence and uniqueness for the natural tax process, which is defined via an integral equation. Our results clarify the existing literature on processes with tax.

Keywords: Risk process; Tax process; Tax rate; Spectrally negative Lévy process; Ruin probability; Tax identity; Optimal control (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:90:y:2020:i:c:p:1-6

DOI: 10.1016/j.insmatheco.2019.10.002

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