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The surplus prior to ruin and the deficit at ruin for a correlated risk process |
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| Authors: | Andrei L Badescu Lothar Breuer Steve Drekic Guy Latouche |
| Institution: | 1. Department of Statistics &2. Actuarial Science , University of Waterloo , Waterloo, Ontario, Canada;3. Department IV-Computer Science , University of Trier , Trier, Germany;4. Département d'Informatique-CP 212 , Université Libre de Bruxelles , Bruxelles, Belgium |
| Abstract: | This paper presents an explicit characterization for the joint probability density function of the surplus immediately prior to ruin and the deficit at ruin for a general risk process, which includes the Sparre-Andersen risk model with phase-type inter-claim times and claim sizes. The model can also accommodate a Markovian arrival process which enables claim sizes to be correlated with the inter-claim times. The marginal density function of the surplus immediately prior to ruin is specifically considered. Several numerical examples are presented to illustrate the application of this result. |
| Keywords: | Surplus immediately prior to ruin Deficit at ruin Sparre-Andersen risk model Phase-type distribution Markovian arrival process Correlated claims Fluid queues Matrix analytic methods |