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

Kiswendsida Mahamoudou OUEDRAOGO; Delwendé Abdoul-Kabir KAFANDO; Francois Xavier OUEDRAOGO; Lassané SAW ADOGO; Pierre Clovis NITIEMA

Kiswendsida Mahamoudou OUEDRAOGO Université Joseph KI ZERBO, 03 BP 7021 Ouagadougou, Burkina Faso
Delwendé Abdoul-Kabir KAFANDO Université Joseph KI ZERBO, 03 BP 7021 Ouagadougou, Burkina Faso; Université Ouaga 3S, 06 BP 10347 Ouagadougou 06, Burkina Faso
Francois Xavier OUEDRAOGO Université Joseph KI ZERBO, 03 BP 7021 Ouagadougou, Burkina Faso
Lassané SAW ADOGO Université Joseph KI ZERBO, 03 BP 7021 Ouagadougou, Burkina Faso
Pierre Clovis NITIEMA Université Thomas SANKARA, 04 BP 8938 Ouagadougou 04, Burkina Faso

Article ID: 2423

Keywords: Gerber-Shiu function; copula; integro-differential equation; ruin probability

Abstract

This article is an extension of the compound Poisson risk model with variable threshold dividend payment strategy to shareholders and a dependence between claims amounts and inter-claim times via Spearman copula. We find the integro-differential equation associated to this risk model.

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.