Approximations for stop-loss reinsurance premiums

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

Research output: Contribution to journalArticleAcademicpeer-review

6 Citations (Scopus)

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
Article number10.1016/j.insmatheco.2005.02.001
Pages (from-to)237-250
Number of pages14
JournalInsurance: mathematics & economics
Volume36
Issue number3
DOIs
Publication statusPublished - 2005

Keywords

  • EWI-12821
  • MSC-62E17
  • MSC-62P05
  • Individual model
  • Aggregate claims
  • stop-loss premium
  • METIS-224164
  • IR-62326
  • Dependent claims

Cite this

Reijnen, R., Albers, WW., & Kallenberg, W. C. M. (2005). Approximations for stop-loss reinsurance premiums. Insurance: mathematics & economics, 36(3), 237-250. [10.1016/j.insmatheco.2005.02.001]. https://doi.org/10.1016/j.insmatheco.2005.02.001
Reijnen, Rajko ; Albers, Willem/Wim ; Kallenberg, W.C.M. / Approximations for stop-loss reinsurance premiums. In: Insurance: mathematics & economics. 2005 ; Vol. 36, No. 3. pp. 237-250.
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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 = "EWI-12821, MSC-62E17, MSC-62P05, Individual model, Aggregate claims, stop-loss premium, METIS-224164, IR-62326, Dependent claims",
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Reijnen, R, Albers, WW & Kallenberg, WCM 2005, 'Approximations for stop-loss reinsurance premiums' Insurance: mathematics & economics, vol. 36, no. 3, 10.1016/j.insmatheco.2005.02.001, pp. 237-250. https://doi.org/10.1016/j.insmatheco.2005.02.001

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

In: Insurance: mathematics & economics, Vol. 36, No. 3, 10.1016/j.insmatheco.2005.02.001, 2005, p. 237-250.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - Approximations for stop-loss reinsurance premiums

AU - Reijnen, Rajko

AU - Albers, Willem/Wim

AU - Kallenberg, W.C.M.

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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 - EWI-12821

KW - MSC-62E17

KW - MSC-62P05

KW - Individual model

KW - Aggregate claims

KW - stop-loss premium

KW - METIS-224164

KW - IR-62326

KW - Dependent claims

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DO - 10.1016/j.insmatheco.2005.02.001

M3 - Article

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SN - 0167-6687

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Reijnen R, Albers WW, Kallenberg WCM. Approximations for stop-loss reinsurance premiums. Insurance: mathematics & economics. 2005;36(3):237-250. 10.1016/j.insmatheco.2005.02.001. https://doi.org/10.1016/j.insmatheco.2005.02.001