Abstract
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.
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Acknowledgements
We give thanks to the anonymous reviewer for his invaluable comments. We are indebted to Prof. K.J. Chen for polishing this paper. The Ministry of Science and Technology, Taiwan, supports this work.
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Hu, CY., Wang, JT. & Cheng, TL. A Characterization of Exponential Distribution in Risk Model. Sankhya A 80, 342–355 (2018). https://doi.org/10.1007/s13171-017-0115-5
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DOI: https://doi.org/10.1007/s13171-017-0115-5