Asymptotic Ruin Probabilities of the Lévy Insurance Model under Periodic Taxation

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. Keywords: Asymptotics; convolution-equivalent tail; Lévy process; periodic taxation; ruin probability; subexponentiality. 1 Introduction The ruin probability of an insurance company is the probability that its surplus process falls below 0 at some time. Recently, the in‡uence of tax payment on the ruin probability has become an interesting problem in actuarial science. Let S = (St)t 0 be a stochastic process, with S0 = x > 0, representing the underlying surplus process in a world without economic factors (tax, reinsurance, or investment, etc.) of an insurance company. Assuming that S is a compound Poisson process with positive drift and that taxes are paid at a …xed rate 2 [0; 1) whenever S is at a running maximum (called the loss-carry-forward taxation), Corresponding author. E-mail: [email protected]; phone: 1-204-474-8710; fax: 1-204-474-7545.