On the moments of the time to ruin in dependent Sparre Andersen models with emphasis on Coxian interclaim times |
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| Institution: | 1. Area of Microbiology, University of León, Campus de Ponferrada, Ponferrada, Spain;2. National Center for Agricultural Utilization Research, United States Department of Agriculture, Peoria, IL, United States;1. School of Sciences, Hebei University of Technology, Tianjin 300401, PR China;2. Department of Mathematics, University of Michigan, Ann Arbor, MI, 48109, USA;1. Faculty of Computer Science & Information Systems, Jazan University, Postal Code 4319 Jazan, Saudi Arabia;2. Department of Applied Mathematics and Informatics, Technical University, Letná 9, 042 00 Ko?ice, Slovakia |
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| Abstract: | The structural properties of the moments of the time to ruin are studied in dependent Sparre Andersen models. The moments of the time to ruin may be viewed as generalized versions of the Gerber–Shiu function. It is shown that structural properties of the Gerber–Shiu function hold also for the moments of the time to ruin. In particular, the moments continue to satisfy defective renewal equations. These properties are discussed in detail in the model of Willmot and Woo (2012), which has Coxian interclaim times and arbitrary time-dependent claim sizes. Structural quantities needed to determine the moments of the time to ruin are specified under this model. Numerical examples illustrating the methodology are presented. |
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| Keywords: | Time to ruin Moment Defective renewal equation Laplace transform Coxian interclaim time |
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