Asymptotic Ruin Probabilities of the Lévy Insurance Model under Periodic Taxation

Abstract

Recently, Albrecher and his coauthors have published a series of papers on the ruin probability of the Lévy insurance model under the so-called loss-carry-forward taxation, meaning that taxes are paid at a certain …xed rate immediately when the surplus of the company is at a running maximum. In this paper we assume periodic taxation under which the company pays tax at a …xed rate on its net income during each period. We devote ourselves to deriving explicit asymptotic relations for the ruin probability in the most general Lévy insurance model in which the Lévy measure has a subexponential tail, a convolution-equivalent tail, or an exponential-like tail.

Convolution equivalent Lévy processes and first passage times

“…The existence of the limit in (4.14) was first proved by Braverman and Samordnitsky [7]. Later, Braverman [6] obtained a complicated description of the limit (see also Albin and Sundén [1], (6.1) and (6.6) and Hao and Tang [18], when Π + X ∈ S (α) (see [29]) it follows from (4.14) that…”

Lévy insurance risk process with Poissonian taxation

“…We additionally assume (1,∞) xν(dx) < ∞ so that X has finite Scandinavian Actuarial Journal 3 In all the aforementioned works concerning taxation, it is implicitly assumed that the insurer's surplus is observed continuously as tax payments are made immediately once the surplus process is at its running maximum. As commented in Hao & Tang (2009), tax is usually collected periodically (e.g. monthly, quarterly or annually) by the tax authority, leading them to study a model in which a fixed portion of the net income (if positive) of each period (of length 1) is paid as tax.…”

A Time-Homogeneous Diffusion Model with Tax

“…Further extensions to the Lévy framework were done by Albrecher et al (2008), Kyprianou and Zhou (2009) and Renaud (2009), among others. See also Hao and Tang (2009) for the study in the Lévy framework but under periodic taxation. So far there is little study beyond the Lévy framework with di¢ culty mainly in the two-sided exit problem.…”