Hostname: page-component-76fb5796d-x4r87 Total loading time: 0 Render date: 2024-04-27T08:20:22.827Z Has data issue: false hasContentIssue false
  • English
  • Français

A Time-Homogeneous Diffusion Model with Tax

Part of: Markov processes Special processes Mathematical economics Applications Stochastic processes

Published online by Cambridge University Press:  30 January 2018

Bin Li ,
Qihe Tang  and
Xiaowen Zhou
Bin Li*
Affiliation:
University of Iowa
Qihe Tang*
Affiliation:
University of Iowa
Xiaowen Zhou*
Affiliation:
Concordia University
*
∗ Postal address: Applied Mathematical and Computational Sciences Program, University of Iowa, 14 MacLean Hall, Iowa City, IA 52242, USA. Email address: bin-li@uiowa.edu
∗∗ Postal address: Department of Statistics and Actuarial Science, University of Iowa, 241 Schaeffer Hall, Iowa City, IA 52242, USA. Email address: qihe-tang@uiowa.edu
∗∗∗ Postal address: Department of Mathematics and Statistics, Concordia University, 1455 de Maisonneuve Blvd. West, Montreal, Quebec, H3G 1M8, Canada. Email address: xzhou@mathstat.concordia.ca
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We study the two-sided exit problem of a time-homogeneous diffusion process with tax payments of loss-carry-forward type and obtain explicit formulae for the Laplace transforms associated with the two-sided exit problem. The expected present value of tax payments until default, the two-sided exit probabilities, and, hence, the nondefault probability with the default threshold equal to the lower bound are solved as immediate corollaries. A sufficient and necessary condition for the tax identity in ruin theory is discovered.

Keywords

Diffusionhitting timeLaplace transformMarkov propertytaxtwo-sided exit problem

MSC classification

Primary: 62P05: Applications to actuarial sciences and financial mathematics
Secondary: 60J60: Diffusion processes 60G40: Stopping times; optimal stopping problems; gambling theory 60K15: Markov renewal processes, semi-Markov processes 91B30: Risk theory, insurance
Type
Research Article
Information
Journal of Applied Probability , Volume 50 , Issue 1 , March 2013 , pp. 195 - 207
Copyright
Copyright © Applied Probability Trust 2013 

References

Albrecher, H. and Hipp, C. (2007). Lundberg's risk process with tax. Bl. DGVFM 28, 13–28.Google Scholar
Albrecher, H., Renaud, J.-F. and Zhou, X. (2008). A Lévy insurance risk process with tax. J. Appl. Prob. 45, 363–375.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, 304–306.Google Scholar
Borodin, A. N. and Salminen, P. (2002). Handbook of Brownian Motion—Facts and Formulae, 2nd edn. Birkhäuser, Basel,Google Scholar
Darling, D. A. and Siegert, A. J. F. (1953). The first passage problem for a continuous Markov process. Ann. Math. Statist. 24, 624–639.Google Scholar
Gīhman, I. Ī. and Skorohod, A. V. (1972). Stochastic Differential Equations. Springer, New York.Google Scholar
Hao, X. and Tang, Q. (2009). Asymptotic ruin probabilities of the Lévy insurance model under periodic taxation. ASTIN Bull. 39, 479–494.CrossRefGoogle Scholar
Klebaner, F. C. (2005). Introduction to Stochastic Calculus with Applications, 2nd edn. Imperial College Press, London.Google Scholar
Kyprianou, A. E. (2006). Introductory Lectures on Fluctuations of Lévy Processes with Applications. Springer, Berlin.Google Scholar
Kyprianou, A. E. and Zhou, X. (2009). General tax structures and the Lévy insurance risk model. J. Appl. Prob. 46, 1146–1156.Google Scholar
Lehoczky, J. P. (1977). Formulas for stopped diffusion processes with stopping times based on the maximum. Ann. Prob. 5, 601–607.Google Scholar
Renaud, J.-F. (2009). The distribution of tax payments in a Lévy insurance risk model with a surplus-dependent taxation structure. Insurance Math. Econom. 45, 242–246.Google Scholar