Asymptotic Ruin Probabilities of the Levy Insurance Model under Periodic Taxation

Recently, Albrecher and his coauthors have published a series of papers on the ruin probability of the Levy insurance model uner the so-called loss-carry-forward taxation, meaning that taxes are paid at a certain fixed 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 fixed rate on its net income during each period. We devote ourselves to deriving explicit asymptotic relations for the ruin probability in the most general Levy insurance model in which the Levy measure has a subexponential tail, a convolution-equivalent tail, or an exponential-like tail.

Keywords: Asymptotics, convolution-equivalent tail, Levy process, periodic taxation, ruin probability, subexponentiality.