On the time and the number of claims when the surplus drops below a certain level. Issue 5 (27th May 2016) - Li, Shuanming; Lu, Yi
Abstract : In this paper, we define to be the first time that the surplus process drops below a certain level from the initial surplus 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 from, and other -related random variables. Explicit expressions for this function, when, and when under exponential claims, are obtained. We then obtain the moments and probability function (with numerical examples) of the number of claims until . We also investigate a joint transform function of the two-sided first exit time and the number of claims until then, and obtain the probability of the surplus hitting an upper level from the initial surplus without having dropped below a lower level with Erlang claims.