## Seminar on Probability and Statistics

Organizer(s) Nakahiro Yoshida, Teppei Ogihara, Yuta Koike

### 2012/10/19

14:50-16:00   Room #006 (Graduate School of Math. Sci. Bldg.)
SHIMIZU, Yasutaka (Graduate School of Engineering Science, Osaka University)
Asymptotic expansion of ruin probability under Lévy insurance risks (JAPANESE)
[ 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 higher-order 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 VaR-type risk measure due to ruin.
[ Reference URL ]
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/09.html