International Journal of Information Engineering and Electronic Business(IJIEEB)

ISSN: 2074-9023 (Print), ISSN: 2074-9031 (Online)

Published By: MECS Press

IJIEEB Vol.2, No.2, Dec. 2010

On a Class of Dual Risk Model with Dependence based on the FGM Copula

Full Text (PDF, 790KB), PP.46-53

Views:54   Downloads:0


Hua Dong,Zaiming Liu

Index Terms

Dividends,dependence,barrier strategies


In this paper, we consider an extension to a dual model under a barrier strategy, in which the innovation sizes depend on the innovation time via the FGM copula. We first derive a renewal equation for the expected total discounted dividends until ruin. Some differential equations and closed-form expressions are given for exponential innovation sizes. Then the optimal dividend barrier and the Laplace transform of the time to ruin are considered. Finally, a numerical example is given.

Cite This Paper

Hua Dong,Zaiming Liu,"On a Class of Dual Risk Model with Dependence based on the FGM Copula", IJIEEB, vol.2, no.2, pp.46-53, 2010.


[1]S. Asmussen, Ruin Probabilities, World Scientific,Singapore, 2000.

[2]H. U. Gerber, E. S. W. Shiu, “The joint distribution of the time of ruin, the surplus immediately before ruin, and the deficit at Ruin”, Insurance: Mathematics and Economics, 1997, 21: 129-137.

[3]H. U. Gerber, E. S. W. Shiu, “On the time value of Ruin”, North America Actuarial Journal, 1998, 2: 48-78.

[4]F. Dufresne, H. U. Gerber, “The surplus immediately before and at ruin, and the amount of the claim causing Ruin”, Insurance: mathematics and Economics, 1988, 7: 193-199.

[5]H. Albrecher, O. J. Boxma, “A ruin model with dependence between claim sizes and intervals”, Insurance: Mathematics and Economics, 2004, 35:245-254.

[6]H. Albrecher, J. Teugels, “Exponential behavior in the presence of dependence in risk Theory”, Journal of Applied Probability, 2006, 43(1): 257-273.

[7]M. Boudreault, H. Cossette, D. Landriault, E.Marceau, “On a risk model with dependence between interclaim arrivals and claim sizes”, Scandinavian Actuarial Journal, 2006, 5: 265-285.

[8]B. DeFinetti, ” Su un'impostazione alternativa della teoria collettiva del rischio”, Transactions of the XV International Congress of Actuaries, 1957, 2: 433-443.

[9]D. C.M.Dickson, H. R. Waters, “Some optimal dividend Problems”, ASTIN Bulletin, 2004, 34: 49-74.

[10]D. Landriault, “ Constant dividend barrier in a risk model with interclaim-dependent claim sizes”, Insurance: Mathematics and Economics, 2008, 42: 31-38.

[11]X. S. Lin, G. E. Willmot, S. Drekic, “The classical risk model with a constant dividend barrier: Analysis of the Gerber-Shiu discounted penalty function”, Insurance: Mathematics and Economics, 2003, 33: 551-566.

[12]X. S. Lin, K. P. Pavlova, “The compound Poisson risk model with a threshold dividend strategy”, Insurance: mathematics and Economics, 2006, 38: 57-80.

[13]H. Albrecher, A. L. Badescu, D. Landriault, “On the dual risk model with tax payments”, Insurance: Mathematics and Economics, 2008, 42: 1086-1094.

[14]B. Avanzi, H. U. Gerber, E. S. W.Shiu, “Optimal dividends in the dual model”, Insurance: Mathematics and Economics,2007, 41: 111-123.

[15]B. Avanzi, H. U. Gerber, “Optimal dividends in the dual model with diffusion”, ASTIN Bulletin, 2008, 38: 653-667.

[16]A. C. Y. Ng, “On a dual model with a dividend threshold”, Insurance: Mathematics and Economics, 2009, 44(2): 315-324.

[17]M. Song, R. Wu, X. Zhang, “Total duration of negative surplus for the dual model”, Applied stochastic model in business and industry 2008 24: 591-600.

[18]R. B. Nelsen, “An introduction to Copulas”, second edition, Springer-Verlag, New York, 2006.

[19]D. C. M. Dickson, C. Hipp, “Ruin probabilities for Erlang(2)risk process”, Insurance: Mathematics and Economics, 1998, 22: 251-262.