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On the ruin probability for nonhomogeneous claims and arbitrary inter-claim revenues. (English) Zbl 1319.91098

Summary: Recently, the authors in [“Recursive calculation of ruin probabilities at or before claim instants for non-identically distributed claims”, ASTIN Bull. 45, No. 2, 421–443 (2015; doi:10.1017/asb.2014.30)] obtained recursive formulas for the ruin probability of a surplus process at or before claim instants under the assumptions that the claim sizes are independent, nonhomogeneous Erlang distributed, and independent of the inter-claim times (i.e., the times between two successive claims), which are assumed to be independent, identically distributed (i.i.d.), following an Erlang or a mixture of exponentials distribution. In this paper, we extend these formulas to the more general case when the inter-claim times are i.i.d. nonnegative random variables following an arbitrary distribution. We also present numerical results based on the new recursions, discuss some computational aspects and state a conjecture that connects the ordering of the claims arrival with the magnitude of the corresponding ruin probabilities.

MSC:

91B30 Risk theory, insurance (MSC2010)
62P05 Applications of statistics to actuarial sciences and financial mathematics
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References:

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