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Distribution of the Present Value of Dividend Payments in a Lévy Risk Model

Part of: Stochastic processes Mathematical economics

Published online by Cambridge University Press:  14 July 2016

Jean-François Renaud  and
Xiaowen Zhou
Jean-François Renaud*
Affiliation:
Université de Montréal
Xiaowen Zhou*
Affiliation:
Concordia University
*
∗ Postal address: Département de Mathématiques et de Statistique, Université de Montréal, C.P. 6128, Succ. Centre-Ville, Montréal, Québec H3C 3J7, Canada. Email address: [email protected]
∗∗ Postal address: Department of Mathematics and Statistics, Concordia University, 1455 de Maisonneuve Blvd W., Montréal, Québec H3G 1M8, Canada. Email address: [email protected]
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Abstract

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In this short paper, we show how fluctuation identities for Lévy processes with no positive jumps yield the distribution of the present value of dividends paid until ruin in a Lévy insurance risk model with a dividend barrier.

Keywords

Lévy processfluctuation theoryscale functionsinsurance risk processdividend barrierdividend paymentstime of ruin

MSC classification

Primary: 60G51: Processes with independent increments; L'evy processes
Secondary: 91B30: Risk theory, insurance
Type
Research Article
Information
Journal of Applied Probability , Volume 44 , Issue 2 , June 2007 , pp. 420 - 427
Copyright
Copyright © Applied Probability Trust 2007 

References

Bertoin, J. (1996). Lévy Processes. Cambridge University Press.Google Scholar
Bertoin, J. (1997). Exponential decay and ergodicity of completely asymmetric Lévy processes in a finite interval. Ann. Appl. Prob. 7, 156–169.CrossRefGoogle Scholar
Chan, T. and Kyprianou, A. E. (2006). Smoothness of scale functions for spectrally negative Lévy processes. Submitted.Google Scholar
Dickson, D. C. M. and Waters, H. R. (2004). Some optimal dividends problems. ASTIN Bull. 34, 49–74.CrossRefGoogle Scholar
Doney, R. A. (2005). Some excursion calculations for spectrally one-sided Lévy processes. In Séminaire de Probabilités XXXVIII (Lecture Notes Math. 1857), Springer, Berlin, pp. 5–15.CrossRefGoogle Scholar
Furrer, H. (1998). Risk processes perturbed by α-stable Lévy motion. Scand. Actuarial J. 1998, 59–74.CrossRefGoogle Scholar
Garrido, J. and Morales, M. (2006). On the expected discounted penalty function for Lévy risk processes. N. Amer. Actuarial J. 10, 196–218.CrossRefGoogle Scholar
Gerber, H. U. and Shiu, E. S. W. (2004). Optimal dividends: analysis with Brownian motion. N. Amer. Actuarial J. 8, 1–20.CrossRefGoogle Scholar
Huzak, M., Perman, M., Šikić, H. and Vondraček, Z. (2004). Ruin probabilities and decompositions for general perturbed risk processes. Ann. Appl. Prob. 14, 1378–1397.CrossRefGoogle Scholar
Klüppelberg, C. and Kyprianou, A. E. (2006). On extreme ruinous behaviour of Lévy insurance risk processes. J. Appl. Prob. 43, 594–598.CrossRefGoogle Scholar
Klüppelberg, C., Kyprianou, A. E. and Maller, R. A. (2004). Ruin probabilities and overshoots for general Lévy insurance risk processes. Ann. Appl. Prob. 14, 1766–1801.CrossRefGoogle Scholar
Kyprianou, A. E. and Palmowski, Z. (2007). Distributional study of de Finetti's dividend problem for a general Lévy insurance risk process. J. Appl. Prob. 44, 428–443 CrossRefGoogle Scholar
Li, S. (2006). The distribution of the dividend payments in the compound Poisson risk model perturbed by a diffusion. Scand. Actuarial J. 2006, 73–85.CrossRefGoogle Scholar
Yang, H. and Zhang, L. (2001). Spectrally negative Lévy processes with applications in risk theory. Adv. Appl. Prob. 33, 281–291.CrossRefGoogle Scholar
Zhou, X. (2006). Discussion on ‘On optimal dividend strategies in the compound Poisson model’ (H. U. Gerber and E. S. W. Shiu). N. Amer. Actuarial J. 10, 79–84.Google Scholar