| Keywords and phrases: Gerber-Shiu function, copula, integro-differential equation, ruin probability.
Received: October 6, 2023; Accepted: November 21, 2023; Published: December 2, 2023
How to cite this article: Kiswendsida Mahamoudou OUEDRAOGO, Delwendé Abdoul-Kabir KAFANDO, Francois Xavier OUEDRAOGO, Lassané SAWADOGO and Pierre Clovis NITIEMA, An integro-differential equation in compound Poisson risk model with variable threshold dividend payment strategy to shareholders and tail dependence between claims amounts and inter-claim time, Advances in Differential Equations and Control Processes 30(4) (2023), 413-429. http://dx.doi.org/10.17654/0974324323023
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References:
[1] H. Cossette, E. Marceau and F. Marri, On a compound Poisson risk model with dependence and in a presence of a constant dividend barrier, Appl. Stoch. Models Bus. Ind. 30(2) (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: Mathematics and Economic 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] Kiswendsida Mahamoudou OUEDRAOGO, Francois Xavier OUEDRAOGO, Delwendé Abdoul-Kabir KAFANDO and Pierre Clovis NITIEMA, On compound risk model with partial premium payment strategy to shareholders and dependence between claim amount and inter-claim times through the Spearman copula, Advances and Applications in Statistics 89(2) (2023), 175-188.
[5] S. Asmussen, Stationary distributions for fluid flow models with or without Brownian noise, Communications in Statistics-Stochastic Models 11 (1995), 21 49.
[6] H. Albrecher and J. Hartinger, On the non-optimality of horizontal barrier strategies in the Sparre Andersen model, HERMES International Journal of Computer Mathematics and its Applications 7 (2006), 1-14.
[7] H. Cosette, E. Marceau and F. Marri, Analysis of ruin measure for the classical compound Poisson risk model with dependence, Scand. Actuar. J. 3 (2010), 221 245.
[8] H. Joe, Multivariate models and dependence concepts, Chapman and Hall/CRC, 1997.
[9] R. B. Nelsen, An Introduction to Copula, Second edition: Springer Series in Statistic, Springer-Verlag, New York, 2006.
[10] W. Hürlimann, Multivariate Frechet copulas and conditional value-at-risqué, Ind. J. Math. Sci. 7 (2004a), 345-364.
[11] M. Boudreault, Modeling and Pricing Earthquake Risk, Scor Canada Actuarial Price, 2003.
[12] H. U. Gerber and E. S. W. Shiu, On the time value of ruin, North American Actuarial Journal (1998), 48-78.
[13] M. Boudreault, H. Cosette, D. Landriault and E. Marceau, On a risk model with dependence between interclaim arrivals and claim sizes, Scandinavian Actuarial Journal 5 (2006), 301-323.
[14] A. K. Nikoloulopoulos and D. Karlis, Fitting copulas to bivariate earthquake data: the seismic gap hypothesis revisited, Environmetrics 19(3) (2008), 251-269.
[15] D. Landriault, Constant dividend barrier in a risk model with interclaim-dependent claim sizes, Insurance: Mathematics and Economics 42(1) (2008), 31-38.
[16] 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: Mathematics and Economics 40(1) (2007), 104-112.
[17] 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: Mathematics and Economics 33(3) (2003), 551-556.
[18] H. U. Gerber, An extension of the renewal equation and its application in the collective theory of risk, Skandinavisk Aktuarietidskrift (1970), 205-210.
[19] H. Albrecher and O. J. Boxma, A ruin model with dependence between claim sizes and claim intervals, Insurance: Mathematics and Economics 35(2) (2004), 245 254.
[20] H. Albrecher and J. Teugels, Exponential behavior in the presence of dependence in risk theory, Journal and Applied Probability 43(1) (2006), 265-285.
[21] H. U. Gerber and E. S. W. Shiu, The time value of ruin in a Sparre Andersen model, North American Actuarial Journal 9(2) (2005), 49-84.
[22] Théorie de la ruine de Patrice BERTAIL et Stéphane LOISEL, CREST- INSEE et MODAL’X, Université Paris Ouest, 2010.
[23] J. Grandell, Aspects of Risk Theory, Springer Series in Statistics: Probability and its Applications, Springer-Verlag, New York, 1991.
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