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Open AccessArticle

Asymptotically Normal Estimators of the Ruin Probability for Lévy Insurance Surplus from Discrete Samples

1
Department of Applied Mathematics, Waseda University, Shinjuku City, Tokyo 169-8555, Japan
2
College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China
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Author to whom correspondence should be addressed.
Risks 2019, 7(2), 37; https://doi.org/10.3390/risks7020037
Received: 11 March 2019 / Revised: 28 March 2019 / Accepted: 29 March 2019 / Published: 3 April 2019
(This article belongs to the Special Issue Loss Models: From Theory to Applications)
A statistical inference for ruin probability from a certain discrete sample of the surplus is discussed under a spectrally negative Lévy insurance risk. We consider the Laguerre series expansion of ruin probability, and provide an estimator for any of its partial sums by computing the coefficients of the expansion. We show that the proposed estimator is asymptotically normal and consistent with the optimal rate of convergence and estimable asymptotic variance. This estimator enables not only a point estimation of ruin probability but also an approximated interval estimation and testing hypothesis. View Full-Text
Keywords: ruin probability; spectrally negative Lévy process; Laguerre polynomial; discrete observations; asymptotic normality ruin probability; spectrally negative Lévy process; Laguerre polynomial; discrete observations; asymptotic normality
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Shimizu, Y.; Zhang, Z. Asymptotically Normal Estimators of the Ruin Probability for Lévy Insurance Surplus from Discrete Samples. Risks 2019, 7, 37.

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