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

Yasutaka Shimizu and Zhimin Zhang
Additional contact information
Yasutaka Shimizu: Department of Applied Mathematics, Waseda University, Shinjuku City, Tokyo 169-8555, Japan
Zhimin Zhang: College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China

Risks, 2019, vol. 7, issue 2, 1-22

Abstract: 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.

Keywords: ruin probability; spectrally negative Lévy process; Laguerre polynomial; discrete observations; asymptotic normality (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (8)

Downloads: (external link)
https://www.mdpi.com/2227-9091/7/2/37/pdf (application/pdf)
https://www.mdpi.com/2227-9091/7/2/37/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jrisks:v:7:y:2019:i:2:p:37-:d:219722

Access Statistics for this article

Risks is currently edited by Mr. Claude Zhang

More articles in Risks from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().