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The density of the time to ruin for a Sparre Andersen process with Erlang arrivals and exponential claims |
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| Authors: | David C. M. Dickson Barry D. Hughes Zhang Lianzeng |
| Affiliation: | 1. Centre for Actuarial Studies, Department of Economics , University of Melbourne , Victoria, 3010, Australia dcmd@unimelb.edu.au;3. Department of Mathematics and Statistics , University of Melbourne , Victoria, 3010, Australia;4. Department of Risk Management and Insurance , Nankai University , Tianjin, 300071, PR China |
| Abstract: | We derive expressions for the density of the time to ruin given that ruin occurs in a Sparre Andersen model in which individual claim amounts are exponentially distributed and inter-arrival times are distributed as Erlang(n,?β). We provide numerical illustrations of finite time ruin probabilities, as well as illustrating features of the density functions. |
| Keywords: | Sparre Anderson models Erlang arrivals exponential claims Laplace transform complex inversion formula finite time ruin moments of time to ruin |