Hostname: page-component-76fb5796d-2lccl Total loading time: 0 Render date: 2024-04-28T00:55:18.927Z Has data issue: false hasContentIssue false
  • English
  • Français

Asymptotic Ruin Probabilities of the Lévy Insurance Model under Periodic Taxation

Published online by Cambridge University Press:  09 August 2013

Xuemiao Hao  and
Qihe Tang
Xuemiao Hao
Affiliation:
Department of Statistics and Actuarial Science, The University of Iowa, 241 Schaeffer Hall, Iowa City, IA 52242, USA Warren Centre for Actuarial Studies and Research, University of Manitoba, 181 Freedman Crescent, Winnipeg, MB R3T 5V4, Canada, E-mail: hao@cc.umanitoba.ca
Qihe Tang
Affiliation:
Department of Statistics and Actuarial Science, The University of Iowa, 241 Schaeffer Hall, Iowa City, IA 52242, USA, E-mail: qtang@stat.uiowa.edu
Get access Rights & Permissions [Opens in a new window]

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 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 Lévy insurance model in which the Lévy measure has a subexponential tail, a convolution-equivalent tail, or an exponential-like tail.

Keywords

Asymptoticsconvolution-equivalent tailLévy processperiodic taxationruin probabilitysubexponentiality
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 39 , Issue 2 , November 2009 , pp. 479 - 494
Copyright
Copyright © International Actuarial Association 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Albin, J.M.P. and Sundén, M. (2009) On the asymptotic behaviour of Lévy processes. Part I: Subexponential and exponential processes. Stochastic Process. Appl. 119(1), 281–304.Google Scholar
Albrecher, H., Badescu, A. and Landriault, D. (2008a) On the dual risk model with tax payments. Insurance Math. Econom. 42(3), 1086–1094.Google Scholar
Albrecher, H., Borst, S., Boxma, O. and Resing, J. (2009) The tax identity in risk theory – a simple proof and an extension. Insurance Math. Econom. 44(2), 304–306.Google Scholar
Albrecher, H. and Hipp, C. (2007) Lundberg's risk process with tax. Bl. DGVFM 28(1), 13–28.Google Scholar
Albrecher, H., Renaud, J.-F. and Zhou, X. (2008b) A Lévy insurance risk process with tax. J. Appl. Probab. 45(2), 363–375.Google Scholar
Asmussen, S. (2000) Ruin Probabilities. World Scientific Publishing Co., Inc., River Edge, NJ.Google Scholar
Braverman, M. (1997) Suprema and sojourn times of Lévy processes with exponential tails. Stochastic Process. Appl. 68(2), 265–283.Google Scholar
Braverman, M. and Samorodnitsky, G. (1995) Functionals of infinitely divisible stochastic processes with exponential tails. Stochastic Process. Appl. 56(2), 207–231.Google Scholar
Chover, J., Ney, P. and Wainger, S. (1973) Functions of probability measures. J. Analyse Math. 26, 255–302.Google Scholar
Doney, R.A. and Kyprianou, A.E. (2006) Overshoots and undershoots of Lévy processes. Ann. Appl. Probab. 16(1), 91–106.Google Scholar
Embrechts, P. and Goldie, C.M. (1982) On convolution tails. Stochastic Process. Appl. 13(3), 263–278.Google Scholar
Hao, X., Tang, Q. and Wei, L. (2009) On the maximum exceedance of a sequence of random variables over a renewal threshold. J. Appl. Probab. 46(2), 559–570.Google Scholar
Klüppelberg, C. (1988) Subexponential distributions and integrated tails. J. Appl. Probab. 25(1), 132–141.Google Scholar
Klüppelberg, C. (1989) Subexponential distributions and characterizations of related classes. Probab. Theory Related Fields 82(2), 259–269.Google Scholar
Klüppelberg, C., Kyprianou, A.E. and Maller, R.A. (2004) Ruin probabilities and overshoots for general Lévy insurance risk processes. Ann. Appl. Probab. 14(4), 1766–1801.Google Scholar
Kyprianou, A.E. (2006) Introductory Lectures on Fluctuations of Lévy Processes with Applications. Springer-Verlag, Berlin.Google Scholar
Palmowski, Z. and Zwart, B. (2007) Tail asymptotics of the supremum of a regenerative process. J. Appl. Probab. 44(2), 349–365.Google Scholar
Rogozin, B.A. (2000) On the constant in the definition of subexponential distributions. Theory Probab. Appl. 44(2), 409–412.Google Scholar
Rosiński, J. and Samorodnitsky, G. (1993) Distributions of subadditive functionals of sample paths of infinitely divisible processes. Ann. Probab. 21(2), 996–1014.Google Scholar
Tang, Q. (2007) The overshoot of a random walk with negative drift. Statist. Probab. Lett. 77(2), 158–165.Google Scholar