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

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 ..