.svg){kind=logo}
LAPLACE TRANSFORM FOR THE COMPOUND POISSON RISK MODEL WITH A STRATEGY OF PARTIAL PAYMENT OF PREMIUMS TO SHAREHOLDERS AND DEPENDENCE BETWEEN CLAIM AMOUNTS AND THE TIME BETWEEN CLAIMS USING THE SPEARMAN COPULA
Keywords:
Gerber-Shiu function, integro-differential equation, Laplace transform, ruin probability.DOI:
https://doi.org/10.17654/0972086324002Abstract
This article is an extension of the compound Poisson risk model with a partial dividend payment strategy to shareholders and dependence between claims amounts and inter-claim times via Spearman copula. We find the Laplace transforms of the Gerber-Shiu function and ultimate ruin probability, associated with this risk model.
Received: September 18, 2023
Accepted: November 21, 2023
References
H. Cossette and E. F. Marceau, On a compound Poisson risk model with dependence and in a presence of a constant dividend barrier, Appl. Stoch. Models Bus. Ind. 30 (2014), 82-98.
S. Heilpern, Ruin measures for a compound Poisson risk model with dependence based on the Spearman copula and the exponential claim sizes, Insurance Math. Econom. 59 (2014), 251-257.
Delwendé Abdoul-Kabir Kafando, Victorien Konané, Frédéric Béré and Pierre Clovis Nitiéma, Extension of the Sparre Andersen via the Spearman copula, Advances and Applications in Statistics 86(1) (2023), 79-100.
S. Asmussen, Stationary distributions for fluid flow models with or without Brownian noise, Comm. Statist. Stochastic Models 11 (1995), 21-49.
S. X. Lin and K. P. Pavlova, The compound Poisson risk model with a threshold dividend strategy, Insurance Math. Econom. 38 (2006), 57-80.
H. Cosette, E. Marceau and F. Marri, Analysis of ruin measure for the classical compound Poisson risk model with dependence, Scand. Actuar. J. 2010 (2010), 221-245.
R. B. Nelsen, An introduction to copula, 2nd ed., Springer Series in Statistic, Springer-Verlag, New York, 2006.
W. Hürlimann, Multivariate Fréchet copulas and conditional value-at-risk, Int. J. Math. Math. Sci. 7 (2004a), 345-364.
M. Boudreault, Modeling and pricing earthquake risk, SCOR Canada Actuarial Price, 2003.
H. U. Gerber and E. S. W. Shiu, On the time value of ruin, North American Actuarial Journal 2 (1998), 48-72.
M. Boudreault, H. Cosette, D. Landriault and E. Marceau, On a risk model with dependence between interclaim arrivals and claim sizes, Scand. Actuar. J. 2006 (2006), 265-285.
A. K. Nikoloulopoulos and D. Karlis, Fitting copulas to bivariate earthquake data: the seismic gap hypothesis revisited, Environmetrics 19(3) (2008), 251-269.
D. Landriault, Constant dividend barrier in a risk model with interclaim-dependent claim sizes, Insurance Math. Econom. 42(1) (2008), 31-38.
K. C. Yue, G. Wang and W. K. Li, The Gerber-Shiu expected discounted penalty function for risk process with interest and a constant dividend barrier, Insurance Math. Econom. 40(1) (2007), 104-112.
X. S. Lin, G. E. Wilmot and S. Drekic, The classical risk model with a constant dividend barrier: analysis of the Gerber-Shiu discounted penalty function, Insurance Math. Econom. 33(3) (2003), 551-556.
H. U. Gerber, An extension of the renewal equation and its application in the collective theory of risk, Scand. Actuar. J. 1970 (1970), 205-210.
H. Albrecher and O. J. Boxma, A ruin model with dependence between claim sizes and claim intervals, Insurance Math. Econom. 35 (2004), 245-254.
Patrice BERTAIL and Stéphane LOISEL, Théorie de la ruine, CREST-INSEE et MODAL’X, Université Paris Ouest, 1991.
Downloads
Published
Issue
Section
License
Copyright (c) 2023 PUSHPA PUBLISHING HOUSE, PRAYAGRAJ, INDIA
This work is licensed under a Creative Commons Attribution 4.0 International License.
____________________________
Attribution: Credit Pusha Publishing House as the original publisher, including title and author(s) if applicable.
Non-Commercial Use: For non-commercial purposes only. No commercial activities without explicit permission.
No Derivatives: Modifying or creating derivative works not allowed without written permission.
Contact Pusha Publishing House for more info or permissions.
