A new look at the homogeneous risk model |
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| Institution: | 1. Département de Mathématique, Université Libre de Bruxelles, Boulevard du Triomphe, Campus de la Plaine C.P.210, B-1050 Bruxelles, Belgium;2. Institut de Science Financière et d’Assurances, Université de Lyon, Université Claude Bernard Lyon 1, 50 Avenue Tony Garnier, F-69007 Lyon, France;1. Department of Statistical Sciences, University of Toronto, Toronto, Ontario M5S 3G3, Canada;2. Quantitative Engineering and Development, TD Securities, Toronto, Ontario M5K 1A2, Canada;3. Department of Statistics and Actuarial Science, University of Iowa, Iowa City, IA 52242, USA |
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| Abstract: | The present paper aims to revisit the homogeneous risk model investigated by De Vylder and Goovaerts, 1999, De Vylder and Goovaerts, 2000. First, a claim arrival process is defined on a fixed time interval by assuming that the arrival times satisfy an order statistic property. Then, the variability and the covariance of an aggregate claim amount process is discussed. The distribution of the aggregate discounted claims is also examined. Finally, a closed-form expression for the non-ruin probability is derived in terms of a family of Appell polynomials. This formula holds for all claim distributions, even dependent. It generalizes several results obtained so far. |
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