Estimation effects on stop-loss premiums under dependence

Willem/Wim Albers, W.C.M. Kallenberg

    Research output: Book/ReportReportProfessional

    21 Downloads (Pure)

    Abstract

    Even a small amount of dependence in large insurance portfolios can lead to huge errors in relevant risk measures, such as stop-loss premiums. This has been shown in a model where the majority consists of ordinary claims and a small fraction of special claims. The special claims are dependent in the sense that a whole group is exposed to damage. In this model, the parameters have to be estimated. The effect of the estimation step is studied here. The estimation error is dominated by the part of the parameters related to the special claims, because by their nature we do not have many observations of them. Although the estimation error in this way is restricted to a few parameters, it turns out that it may be quite substantial. Upper and lower confidence bounds are given for the stop-loss premium, thus protecting against the estimation effect.
    Original languageUndefined
    Place of PublicationEnschede
    PublisherUniversity of Twente, Department of Applied Mathematics
    Number of pages24
    Publication statusPublished - May 2007

    Publication series

    Name
    PublisherDepartment of Applied Mathematics, University of Twente
    No.P2773/1837
    ISSN (Print)1874-4850
    ISSN (Electronic)1874-4850

    Keywords

    • IR-67130
    • Aggregate claims
    • stop-loss premium
    • Dependent claims
    • METIS-241632
    • MSC-62F10
    • confidence bounds
    • EWI-9921
    • MSC-62P05
    • MSC-62E17
    • Estimation error

    Cite this

    Albers, WW., & Kallenberg, W. C. M. (2007). Estimation effects on stop-loss premiums under dependence. Enschede: University of Twente, Department of Applied Mathematics.
    Albers, Willem/Wim ; Kallenberg, W.C.M. / Estimation effects on stop-loss premiums under dependence. Enschede : University of Twente, Department of Applied Mathematics, 2007. 24 p.
    @book{0624f295403f40f68dc2f78b80aed1e8,
    title = "Estimation effects on stop-loss premiums under dependence",
    abstract = "Even a small amount of dependence in large insurance portfolios can lead to huge errors in relevant risk measures, such as stop-loss premiums. This has been shown in a model where the majority consists of ordinary claims and a small fraction of special claims. The special claims are dependent in the sense that a whole group is exposed to damage. In this model, the parameters have to be estimated. The effect of the estimation step is studied here. The estimation error is dominated by the part of the parameters related to the special claims, because by their nature we do not have many observations of them. Although the estimation error in this way is restricted to a few parameters, it turns out that it may be quite substantial. Upper and lower confidence bounds are given for the stop-loss premium, thus protecting against the estimation effect.",
    keywords = "IR-67130, Aggregate claims, stop-loss premium, Dependent claims, METIS-241632, MSC-62F10, confidence bounds, EWI-9921, MSC-62P05, MSC-62E17, Estimation error",
    author = "Willem/Wim Albers and W.C.M. Kallenberg",
    note = "eemcs-eprint-9921",
    year = "2007",
    month = "5",
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    publisher = "University of Twente, Department of Applied Mathematics",
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    Albers, WW & Kallenberg, WCM 2007, Estimation effects on stop-loss premiums under dependence. University of Twente, Department of Applied Mathematics, Enschede.

    Estimation effects on stop-loss premiums under dependence. / Albers, Willem/Wim; Kallenberg, W.C.M.

    Enschede : University of Twente, Department of Applied Mathematics, 2007. 24 p.

    Research output: Book/ReportReportProfessional

    TY - BOOK

    T1 - Estimation effects on stop-loss premiums under dependence

    AU - Albers, Willem/Wim

    AU - Kallenberg, W.C.M.

    N1 - eemcs-eprint-9921

    PY - 2007/5

    Y1 - 2007/5

    N2 - Even a small amount of dependence in large insurance portfolios can lead to huge errors in relevant risk measures, such as stop-loss premiums. This has been shown in a model where the majority consists of ordinary claims and a small fraction of special claims. The special claims are dependent in the sense that a whole group is exposed to damage. In this model, the parameters have to be estimated. The effect of the estimation step is studied here. The estimation error is dominated by the part of the parameters related to the special claims, because by their nature we do not have many observations of them. Although the estimation error in this way is restricted to a few parameters, it turns out that it may be quite substantial. Upper and lower confidence bounds are given for the stop-loss premium, thus protecting against the estimation effect.

    AB - Even a small amount of dependence in large insurance portfolios can lead to huge errors in relevant risk measures, such as stop-loss premiums. This has been shown in a model where the majority consists of ordinary claims and a small fraction of special claims. The special claims are dependent in the sense that a whole group is exposed to damage. In this model, the parameters have to be estimated. The effect of the estimation step is studied here. The estimation error is dominated by the part of the parameters related to the special claims, because by their nature we do not have many observations of them. Although the estimation error in this way is restricted to a few parameters, it turns out that it may be quite substantial. Upper and lower confidence bounds are given for the stop-loss premium, thus protecting against the estimation effect.

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    KW - stop-loss premium

    KW - Dependent claims

    KW - METIS-241632

    KW - MSC-62F10

    KW - confidence bounds

    KW - EWI-9921

    KW - MSC-62P05

    KW - MSC-62E17

    KW - Estimation error

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    PB - University of Twente, Department of Applied Mathematics

    CY - Enschede

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    Albers WW, Kallenberg WCM. Estimation effects on stop-loss premiums under dependence. Enschede: University of Twente, Department of Applied Mathematics, 2007. 24 p.