Parametric inference for ruin probability in the classical risk model

Takayoshi Oshime, Yasutaka Shimizu

    Research output: Contribution to journalArticle

    Abstract

    Consider the classical insurance surplus model with a parametric family for the claim distribution. Although we can construct an asymptotically normal estimator of the ruin probability from the claim data, the asymptotic variance is not easy to estimate since it includes the derivative of the ruin probability with respect to the parameter. This paper gives an explicit asymptotic formula for the asymptotic variance, which is easy to estimate, and gives an asymptotic confidence interval of ruin probability.

    Original languageEnglish
    Pages (from-to)28-37
    Number of pages10
    JournalStatistics and Probability Letters
    Volume133
    DOIs
    Publication statusPublished - 2018 Feb 1

    Fingerprint

    Parametric Inference
    Ruin Probability
    Asymptotic Variance
    Probability of Ruin
    Asymptotic Formula
    Insurance
    Estimate
    Confidence interval
    Explicit Formula
    Estimator
    Derivative
    Model
    Ruin probability
    Asymptotic variance
    Classical risk model
    Inference
    Family
    Probability of ruin
    Derivatives
    Surplus

    Keywords

    • Asymptotic confidence interval
    • Cramér approximation
    • Delta method
    • Ruin probability
    • Small claims

    ASJC Scopus subject areas

    • Statistics and Probability
    • Statistics, Probability and Uncertainty

    Cite this

    Parametric inference for ruin probability in the classical risk model. / Oshime, Takayoshi; Shimizu, Yasutaka.

    In: Statistics and Probability Letters, Vol. 133, 01.02.2018, p. 28-37.

    Research output: Contribution to journalArticle

    @article{e6fd33237a1144bdad9ca8eddc12fdca,
    title = "Parametric inference for ruin probability in the classical risk model",
    abstract = "Consider the classical insurance surplus model with a parametric family for the claim distribution. Although we can construct an asymptotically normal estimator of the ruin probability from the claim data, the asymptotic variance is not easy to estimate since it includes the derivative of the ruin probability with respect to the parameter. This paper gives an explicit asymptotic formula for the asymptotic variance, which is easy to estimate, and gives an asymptotic confidence interval of ruin probability.",
    keywords = "Asymptotic confidence interval, Cram{\'e}r approximation, Delta method, Ruin probability, Small claims",
    author = "Takayoshi Oshime and Yasutaka Shimizu",
    year = "2018",
    month = "2",
    day = "1",
    doi = "10.1016/j.spl.2017.09.020",
    language = "English",
    volume = "133",
    pages = "28--37",
    journal = "Statistics and Probability Letters",
    issn = "0167-7152",
    publisher = "Elsevier",

    }

    TY - JOUR

    T1 - Parametric inference for ruin probability in the classical risk model

    AU - Oshime, Takayoshi

    AU - Shimizu, Yasutaka

    PY - 2018/2/1

    Y1 - 2018/2/1

    N2 - Consider the classical insurance surplus model with a parametric family for the claim distribution. Although we can construct an asymptotically normal estimator of the ruin probability from the claim data, the asymptotic variance is not easy to estimate since it includes the derivative of the ruin probability with respect to the parameter. This paper gives an explicit asymptotic formula for the asymptotic variance, which is easy to estimate, and gives an asymptotic confidence interval of ruin probability.

    AB - Consider the classical insurance surplus model with a parametric family for the claim distribution. Although we can construct an asymptotically normal estimator of the ruin probability from the claim data, the asymptotic variance is not easy to estimate since it includes the derivative of the ruin probability with respect to the parameter. This paper gives an explicit asymptotic formula for the asymptotic variance, which is easy to estimate, and gives an asymptotic confidence interval of ruin probability.

    KW - Asymptotic confidence interval

    KW - Cramér approximation

    KW - Delta method

    KW - Ruin probability

    KW - Small claims

    UR - http://www.scopus.com/inward/record.url?scp=85033447781&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=85033447781&partnerID=8YFLogxK

    U2 - 10.1016/j.spl.2017.09.020

    DO - 10.1016/j.spl.2017.09.020

    M3 - Article

    VL - 133

    SP - 28

    EP - 37

    JO - Statistics and Probability Letters

    JF - Statistics and Probability Letters

    SN - 0167-7152

    ER -