Estimating Gerber–Shiu functions from discretely observed Lévy driven surplus

Yasutaka Shimizu, Zhimin Zhang

    Research output: Contribution to journalArticle

    14 Citations (Scopus)

    Abstract

    Consider an insurance surplus process driven by a Lévy subordinator, which is observed at discrete time points. An estimator of the Gerber–Shiu function is proposed via the empirical Fourier transform of the Gerber–Shiu function. By evaluating its mean squared error, we show the L2-consistency of the estimator under the assumption of high-frequency observation of the surplus process in a long term. Simulation studies are also presented to show the finite sample performance of the proposed estimator.

    Original languageEnglish
    Pages (from-to)84-98
    Number of pages15
    JournalInsurance: Mathematics and Economics
    Volume74
    DOIs
    Publication statusPublished - 2017 May 1

    Fingerprint

    Gerber-Shiu Function
    Estimating Function
    Estimator
    Subordinator
    Mean Squared Error
    Insurance
    Fourier transform
    Discrete-time
    Simulation Study
    Term
    Gerber-Shiu function
    Surplus
    Surplus process

    Keywords

    • Estimation
    • Fourier inversion
    • Gerber–Shiu function
    • L-consistency
    • Lévy risk model

    ASJC Scopus subject areas

    • Statistics and Probability
    • Economics and Econometrics
    • Statistics, Probability and Uncertainty

    Cite this

    Estimating Gerber–Shiu functions from discretely observed Lévy driven surplus. / Shimizu, Yasutaka; Zhang, Zhimin.

    In: Insurance: Mathematics and Economics, Vol. 74, 01.05.2017, p. 84-98.

    Research output: Contribution to journalArticle

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