Asymptotically normal estimators of the ruin probability for lévy insurance surplus from discrete samples

Yasutaka Shimizu, Zhimin Zhang

Research output: Contribution to journalArticle

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.

Original languageEnglish
Article number37
JournalRisks
Volume7
Issue number2
DOIs
Publication statusPublished - 2019 Jun 1

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Keywords

  • Asymptotic normality
  • Discrete observations
  • Laguerre polynomial
  • Ruin probability
  • Spectrally negative Lévy process

ASJC Scopus subject areas

  • Accounting
  • Economics, Econometrics and Finance (miscellaneous)
  • Strategy and Management

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