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On a conjecture related to the ruin probability for nonhomogeneous exponentially distributed claims
Authors:Ani?oara Maria R?ducan  Gheorghi?? Zb?ganu
Institution:1. Institute for Mathematical Statistics and Applied Mathematics, Bucharest, Romania.;2. Faculty of Mathematics and Computer Science, University of Bucharest, Bucharest, Romania.
Abstract:Recently, some recursive formulas have been obtained for the ruin probability evaluated at or before claim instants for a surplus process under the assumptions that the claim sizes are independent, nonhomogeneous Erlang distributed, and independent of the inter-claim revenues, which are assumed to be independent, identically distributed, following an arbitrary distribution. Based on numerical examples, a conjecture has also been stated relating the order in which the claims arrive to the magnitude of the corresponding ruin probability. In this paper, we prove this conjecture in the particular case when the claims are all exponentially distributed with different parameters.
Keywords:Surplus process  ruin probability  nonhomogeneous claim sizes  exponential distribution  claims order  recursions
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