A Markov additive risk process in dimension 2 perturbed by a fractional Brownian motion |
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Authors: | Landy Rabehasaina |
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Affiliation: | Laboratoire de Mathématiques, Université de Franche Comté, UFR ST, 16 route de Gray, 25030 Besançon cédex, France |
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Abstract: | We consider the following theoretical reinsurance ruin problem. An insurance company has two types of independent claims, respectively modeled by a Markov additive process (large claims) and a fractional Brownian motion (small claims) with Hurst parameter H∈[1/2,1), and chooses to reinsure both of them according to a quota share policy. This leads to studying a bivariate risk process. We study two types of ruins, corresponding to either ruin of one of the risk processes, or of both. We obtain asymptotics of the corresponding ruin probabilities when initial reserves tend to infinity along a direction. |
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Keywords: | 60J25 60G22 60K30 |
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