Approximations for stop-loss reinsurance premiums

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

    Research output: Book/ReportReportProfessional

    104 Downloads (Pure)

    Abstract

    Various approximations of stop-loss reinsurance premiums are described in literature. For a wide variety of claim size distributions and retention levels, such approximations are compared in this paper to each other, as well as to a quantitative criterion. For the aggregate claims two models are used, both involving various model parameters. In the first model the claims are simply independent, while a certain dependence structure is assumed in the second model. A relatively simple rule of thumb is formulated for choosing the best approximation for either model. This approximation satisfies the aforementioned criterion. Finally, by comparing the two models, it is demonstrated that a small degree of dependence between the claims already has a substantial effect on the stop-loss premiums. The difference can run up to a factor 500.
    Original languageUndefined
    Place of PublicationEnschede
    PublisherUniversity of Twente, Faculty of Mathematical Sciences
    Number of pages15
    Publication statusPublished - 2003

    Publication series

    NameMemorandum Faculty of Mathematical Sciences
    PublisherDepartment of Applied Mathematics, University of Twente
    No.1695
    ISSN (Print)0169-2690

    Keywords

    • MSC-62P05
    • EWI-3515
    • IR-65880
    • METIS-213198
    • MSC-62E17

    Cite this

    Reijnen, R., Albers, WW., & Kallenberg, W. C. M. (2003). Approximations for stop-loss reinsurance premiums. (Memorandum Faculty of Mathematical Sciences; No. 1695). Enschede: University of Twente, Faculty of Mathematical Sciences.
    Reijnen, R. ; Albers, Willem/Wim ; Kallenberg, W.C.M. / Approximations for stop-loss reinsurance premiums. Enschede : University of Twente, Faculty of Mathematical Sciences, 2003. 15 p. (Memorandum Faculty of Mathematical Sciences; 1695).
    @book{7fb2409d8ea04d7a8d6cd07df2e8a288,
    title = "Approximations for stop-loss reinsurance premiums",
    abstract = "Various approximations of stop-loss reinsurance premiums are described in literature. For a wide variety of claim size distributions and retention levels, such approximations are compared in this paper to each other, as well as to a quantitative criterion. For the aggregate claims two models are used, both involving various model parameters. In the first model the claims are simply independent, while a certain dependence structure is assumed in the second model. A relatively simple rule of thumb is formulated for choosing the best approximation for either model. This approximation satisfies the aforementioned criterion. Finally, by comparing the two models, it is demonstrated that a small degree of dependence between the claims already has a substantial effect on the stop-loss premiums. The difference can run up to a factor 500.",
    keywords = "MSC-62P05, EWI-3515, IR-65880, METIS-213198, MSC-62E17",
    author = "R. Reijnen and Willem/Wim Albers and W.C.M. Kallenberg",
    note = "Imported from MEMORANDA",
    year = "2003",
    language = "Undefined",
    series = "Memorandum Faculty of Mathematical Sciences",
    publisher = "University of Twente, Faculty of Mathematical Sciences",
    number = "1695",

    }

    Reijnen, R, Albers, WW & Kallenberg, WCM 2003, Approximations for stop-loss reinsurance premiums. Memorandum Faculty of Mathematical Sciences, no. 1695, University of Twente, Faculty of Mathematical Sciences, Enschede.

    Approximations for stop-loss reinsurance premiums. / Reijnen, R.; Albers, Willem/Wim; Kallenberg, W.C.M.

    Enschede : University of Twente, Faculty of Mathematical Sciences, 2003. 15 p. (Memorandum Faculty of Mathematical Sciences; No. 1695).

    Research output: Book/ReportReportProfessional

    TY - BOOK

    T1 - Approximations for stop-loss reinsurance premiums

    AU - Reijnen, R.

    AU - Albers, Willem/Wim

    AU - Kallenberg, W.C.M.

    N1 - Imported from MEMORANDA

    PY - 2003

    Y1 - 2003

    N2 - Various approximations of stop-loss reinsurance premiums are described in literature. For a wide variety of claim size distributions and retention levels, such approximations are compared in this paper to each other, as well as to a quantitative criterion. For the aggregate claims two models are used, both involving various model parameters. In the first model the claims are simply independent, while a certain dependence structure is assumed in the second model. A relatively simple rule of thumb is formulated for choosing the best approximation for either model. This approximation satisfies the aforementioned criterion. Finally, by comparing the two models, it is demonstrated that a small degree of dependence between the claims already has a substantial effect on the stop-loss premiums. The difference can run up to a factor 500.

    AB - Various approximations of stop-loss reinsurance premiums are described in literature. For a wide variety of claim size distributions and retention levels, such approximations are compared in this paper to each other, as well as to a quantitative criterion. For the aggregate claims two models are used, both involving various model parameters. In the first model the claims are simply independent, while a certain dependence structure is assumed in the second model. A relatively simple rule of thumb is formulated for choosing the best approximation for either model. This approximation satisfies the aforementioned criterion. Finally, by comparing the two models, it is demonstrated that a small degree of dependence between the claims already has a substantial effect on the stop-loss premiums. The difference can run up to a factor 500.

    KW - MSC-62P05

    KW - EWI-3515

    KW - IR-65880

    KW - METIS-213198

    KW - MSC-62E17

    M3 - Report

    T3 - Memorandum Faculty of Mathematical Sciences

    BT - Approximations for stop-loss reinsurance premiums

    PB - University of Twente, Faculty of Mathematical Sciences

    CY - Enschede

    ER -

    Reijnen R, Albers WW, Kallenberg WCM. Approximations for stop-loss reinsurance premiums. Enschede: University of Twente, Faculty of Mathematical Sciences, 2003. 15 p. (Memorandum Faculty of Mathematical Sciences; 1695).