Title: A Characterization of Exponential Distribution in Risk Model

Author(s): Chin-Yuan Hu, Jheng-Tinng Wang and Tsung-Lin Cheng
Issue: Volume 80 Series A Part 2 Year 2018
Pages: 342 -- 355
In the general risk model (or the Sparre-Andersen model), it is well-known that the following assertion holds: if the claim size is exponentially distributed then the non-ruin probability distribution is a mixture of exponential distributions. In this paper, under some general conditions, we prove that the converse statement of the previous assertion is also true. Besides, we define a new non-ruin measure associated with the aggregate logarithms of the claim-over-profit ratios and obtain a result on Pareto-type distributions.
AMS (2000) subject classification. Primary: 62E10; Secondary: 60G50.
Keywords and phrases: Characterization, Erlang distribution, Exponential distributions, Gamma function, Risk model.