Journal article

On the time and the number of claims when the surplus drops below a certain level

Shuanming Li, Yi Lu

Scandinavian Actuarial Journal | TAYLOR & FRANCIS LTD | Published : 2016

Abstract

In this paper, we define (Formula presented.) to be the first time that the surplus process drops below a certain level (Formula presented.) from the initial surplus (Formula presented.) for a risk model with interest. A generalized Gerber–Shiu-type function is then defined based on the first time and the number of claims that the surplus drops below (Formula presented.) from (Formula presented.) , and other (Formula presented.) -related random variables. Explicit expressions for this function, when (Formula presented.) , and when (Formula presented.) under exponential claims, are obtained. We then obtain the moments and probability function (with numerical examples) of the number of claims ..

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University of Melbourne Researchers

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Funding Acknowledgements

The authors would like to thank two anonymous referees for their valuable comments and suggestions to improve the paper. The authors would also like to thank Mr. Simon Mak for his help on the numerical calculation of examples in Section 3.4. This research for Dr. Yi Lu was supported by the Natural Science and Engineering Research Council (NSERC) of Canada.