Some asymptotic results for transient random walks with applications to insurance risk (Q2731155)
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scientific article; zbMATH DE number 1625611
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Some asymptotic results for transient random walks with applications to insurance risk |
scientific article; zbMATH DE number 1625611 |
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Some asymptotic results for transient random walks with applications to insurance risk (English)
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21 April 2002
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heavy-tailed step distribution
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asymptotic behavior
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first passage time
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ruin probability
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The author considers a real-valued random walk which drifts to \(-\infty\) and is such that the step distribution is heavy-tailed, e.g. sub-exponential. He derives some new results on the asymptotic behavior of the distribution of the upwards first passage time, and, as an application, he obtains a new proof of the exact rate of convergence for the ruin probability after time \(t\).
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