Keywords and phrases: Gerber-Shiu function, integro-differential equation, Laplace transform, ruin probability.
Received: September 18, 2023; Accepted: November 21, 2023; Published: December 6, 2023
How to cite this article: Kiswendsida Mahamoudou OUEDRAOGO, Delwendé Abdoul-Kabir KAFANDO, Lassané SAWADOGO, Francois Xavier OUEDRAOGO and Pierre Clovis NITIEMA, 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, Far East Journal of Theoretical Statistics 68(1) (2024), 23-39. http://dx.doi.org/10.17654/0972086324002
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
References:
[1] 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. [2] 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. [3] 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. [4] S. Asmussen, Stationary distributions for fluid flow models with or without Brownian noise, Comm. Statist. Stochastic Models 11 (1995), 21-49. [5] S. X. Lin and K. P. Pavlova, The compound Poisson risk model with a threshold dividend strategy, Insurance Math. Econom. 38 (2006), 57-80. [6] 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. [7] R. B. Nelsen, An introduction to copula, 2nd ed., Springer Series in Statistic, Springer-Verlag, New York, 2006. [8] W. Hürlimann, Multivariate Fréchet copulas and conditional value-at-risk, Int. J. Math. Math. Sci. 7 (2004a), 345-364. [9] M. Boudreault, Modeling and pricing earthquake risk, SCOR Canada Actuarial Price, 2003. [10] H. U. Gerber and E. S. W. Shiu, On the time value of ruin, North American Actuarial Journal 2 (1998), 48-72. [11] 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. [12] A. K. Nikoloulopoulos and D. Karlis, Fitting copulas to bivariate earthquake data: the seismic gap hypothesis revisited, Environmetrics 19(3) (2008), 251-269. [13] D. Landriault, Constant dividend barrier in a risk model with interclaim-dependent claim sizes, Insurance Math. Econom. 42(1) (2008), 31-38. [14] 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. [15] 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. [16] 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. [17] H. Albrecher and O. J. Boxma, A ruin model with dependence between claim sizes and claim intervals, Insurance Math. Econom. 35 (2004), 245-254. [18] Patrice BERTAIL and Stéphane LOISEL, Théorie de la ruine, CREST-INSEE et MODAL’X, Université Paris Ouest, 1991.
|