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The deficit at ruin in the stationary renewal risk model |
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| Authors: | Gordon Willmot |
| Institution: | 1. Department of Statistical and Actuarial Sciences , University of Western Ontario , London , Ontario , Canada , N6A 5B7 ahassan@stats.uwo.ca;3. Département de mathématiques et de statistique , Université de Montréal , Montréal , Québec , Canada , H3C 3J7 |
| Abstract: | Properties of the distribution of the deficit at ruin in the stationary renewal risk model are studied. A mixture representation for the conditional distribution of the deficit at ruin (given that ruin occurs) is derived, as well as a stochastic decomposition involving the residual lifetime associated with the maximal aggregate loss. When the individual claims have a phase-type distribution, the deficit at ruin is also of phase-type. |
| Keywords: | Sparre Andersen model ladder height maximal aggregate loss compound geometric convolution defective renewal equation phase-type distribution DFR |