On a Class of Dual Risk Model with Dependence based on the FGM Copula
Автор: Hua Dong, Zaiming Liu
Журнал: International Journal of Information Engineering and Electronic Business(IJIEEB) @ijieeb
Статья в выпуске: 2 vol.2, 2010 года.
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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.
Dividends, dependence, barrier strategies
Короткий адрес: https://sciup.org/15013056
IDR: 15013056
Список литературы On a Class of Dual Risk Model with Dependence based on the FGM Copula
- S. Asmussen, Ruin Probabilities, World Scientific,Singapore, 2000.
- 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.
- H. U. Gerber, E. S. W. Shiu, “On the time value of Ruin”, North America Actuarial Journal, 1998, 2: 48-78.
- 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.
- H. Albrecher, O. J. Boxma, “A ruin model with dependence between claim sizes and intervals”, Insurance: Mathematics and Economics, 2004, 35:245-254.
- H. Albrecher, J. Teugels, “Exponential behavior in the presence of dependence in risk Theory”, Journal of Applied Probability, 2006, 43(1): 257-273.
- 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.
- B. DeFinetti, ” Su un'impostazione alternativa della teoria collettiva del rischio”, Transactions of the XV International Congress of Actuaries, 1957, 2: 433-443.
- D. C.M.Dickson, H. R. Waters, “Some optimal dividend Problems”, ASTIN Bulletin, 2004, 34: 49-74.
- D. Landriault, “ Constant dividend barrier in a risk model with interclaim-dependent claim sizes”, Insurance: Mathematics and Economics, 2008, 42: 31-38.
- 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.
- X. S. Lin, K. P. Pavlova, “The compound Poisson risk model with a threshold dividend strategy”, Insurance: mathematics and Economics, 2006, 38: 57-80.
- H. Albrecher, A. L. Badescu, D. Landriault, “On the dual risk model with tax payments”, Insurance: Mathematics and Economics, 2008, 42: 1086-1094.
- B. Avanzi, H. U. Gerber, E. S. W.Shiu, “Optimal dividends in the dual model”, Insurance: Mathematics and Economics,2007, 41: 111-123.
- B. Avanzi, H. U. Gerber, “Optimal dividends in the dual model with diffusion”, ASTIN Bulletin, 2008, 38: 653-667.
- A. C. Y. Ng, “On a dual model with a dividend threshold”, Insurance: Mathematics and Economics, 2009, 44(2): 315-324.
- 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.
- R. B. Nelsen, “An introduction to Copulas”, second edition, Springer-Verlag, New York, 2006.
- D. C. M. Dickson, C. Hipp, “Ruin probabilities for Erlang(2)risk process”, Insurance: Mathematics and Economics, 1998, 22: 251-262.
