Conditional Recursive Equations on Excess-of-Loss Reinsurance

YANG Jing-ping; WANG Xiao-qian; CHENG Shi-hong

Volume 27 Issue 8

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Article Navigation > Applied Mathematics and Mechanics > 2006 > 27(8): 931-939

YANG Jing-ping, WANG Xiao-qian, CHENG Shi-hong. Conditional Recursive Equations on Excess-of-Loss Reinsurance[J]. Applied Mathematics and Mechanics, 2006, 27(8): 931-939.

Citation:

YANG Jing-ping, WANG Xiao-qian, CHENG Shi-hong. Conditional Recursive Equations on Excess-of-Loss Reinsurance[J]. Applied Mathematics and Mechanics, 2006, 27(8): 931-939.

Citation:

YANG Jing-ping, WANG Xiao-qian, CHENG Shi-hong. Conditional Recursive Equations on Excess-of-Loss Reinsurance[J]. Applied Mathematics and Mechanics, 2006, 27(8): 931-939.

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Conditional Recursive Equations on Excess-of-Loss Reinsurance

1.
LMAM, School of Mathematical Sciences, Peking University, Bejing 100871, P. R. China;

Received Date: 2004-09-24
Rev Recd Date: 2006-04-26
Publish Date: 2006-08-15

Abstract

Abstract

The marginal recursive equations on excess-of-loss reinsurance treaty were investigated,under the assumption that the number of claims belongs to the family consisting of Poisson,binomial and negative binomial,and that the severity distribution had bounded continuous density function.On condition of the numbers of claims associated with the the reinsurer and the cedent,some recursive equations are obtained for the marginal distributions of the total payments of the reinsurer and the cedent.
- Panjer recursion,
- Poisson distribution,
- binomial distribution,
- negative binomial distribution,
- excess-of-loss reinsurance

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References(6)

References

[1]	Sundt B.On multivariate panjer recursions[J].Astin Bulletin,1999,29(1):29—45. doi: 10.2143/AST.29.1.504605
[2]	YANG Jing-ping,CHENG Shi-hong,WANG Xiao-qian.Bivariate recursive equations on excess-of-loss reinsurance[J/OL]. Acta Mathematica Sinica,English Series. doi: 10.10071510114-005-0722-2,2006-04-02.
[3]	Sundt B,Jewell W S. Further results of recursive evaluation of compound risk models[J].Astin Bulletin,1981,12(1):27—39.
[4]	Lemaire J.Bonus-Malus Systems in Automobile Insurance[M].Boston: Kluwer Academic Publishers,1995.
[5]	Hesselager O.Recursions for certain bivariate counting distributions and their compound distributions[J].Astin Bulletin,1996,26(1):35—52. doi: 10.2143/AST.26.1.563232
[6]	Panjer H H.Recursive evaluation of a family of compound distributions[J].Astin Bulletin,1981,12(1):22—26.

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