統計数学セミナー
Seminar on Probability and Statistics 
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Seminar on Probability and Statistics Friday October 19 2012 Tokyo 006 2:504:00 pm
Asymptotic expansion of ruin probability under Lévy insurance risks
清水 泰隆 / SHIMIZU, Yasutaka 大阪大学大学院基礎工学研究科 / Graduate School of Engineering Science, Osaka University Abstract An asymptotic expansion formula of the ultimate ruin probability under L'evy insurance risks
is given as the loading factor tends to zero. The formula is obtained via the Edgeworth type expansion of
the compound geometric random sum. We give higherorder expansions of the ruin probability with a certain validity.
This allows us to evaluate quantile of the ruin function, which is nicely applied to estimate the VaRtype risk measure due to ruin.

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Seminar on Probability and Statistics 