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Relative Importance of Risk Sources in Insurance Systems

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  • Edward Frees

Abstract

Actuaries, and other managers of uncertainty, identify factors in modeling insurance risks because they believe (1) that these factors affect the outcome of a risk or (2) that the factors can be managed, thus allowing analysts a degree of control over the insurance system. This paper shows how to use a statistical measure, the coefficient of determination, for quantifying the relative importance of a source of uncertainty. With a quantitative measure of relative importance, risk managers can sharpen their intuition about the relative importance of risk factors and become better custodians of financial security systems.This paper shows that the coefficient of determination is intuitively appealing in assessing the effectiveness of basic risk management techniques including risk exchange, pooling, and financial risk management. A single source common to all risks reduces the effectiveness of a pool; the risk measure quantifies the relative importance of this common source. The coefficient of determination is shown to have roots in the economics as well as the statistics literature. This connection provides further motivation for using the coefficient of determination and also suggests alternative measures for quantifying relative importance. The risk measure is useful in multivariate situations in which several factors affect a risk simultaneously. The paper illustrates this usefulness by considering a pool of policies that is subject to mortality, a common disaster, and a common investment environment.

Suggested Citation

  • Edward Frees, 1998. "Relative Importance of Risk Sources in Insurance Systems," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(2), pages 34-49.
  • Handle: RePEc:taf:uaajxx:v:2:y:1998:i:2:p:34-49
    DOI: 10.1080/10920277.1998.10595694
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    Cited by:

    1. Karabey, Uǧur & Kleinow, Torsten & Cairns, Andrew J.G., 2014. "Factor risk quantification in annuity models," Insurance: Mathematics and Economics, Elsevier, vol. 58(C), pages 34-45.
    2. Shengkun Xie, 2021. "Improving Explainability of Major Risk Factors in Artificial Neural Networks for Auto Insurance Rate Regulation," Risks, MDPI, vol. 9(7), pages 1-21, July.
    3. Mahmoud Hamada & Emiliano A. Valdez, 2008. "CAPM and Option Pricing With Elliptically Contoured Distributions," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 75(2), pages 387-409, June.
    4. Rabitti, Giovanni & Borgonovo, Emanuele, 2020. "Is mortality or interest rate the most important risk in annuity models? A comparison of sensitivity analysis methods," Insurance: Mathematics and Economics, Elsevier, vol. 95(C), pages 48-58.
    5. repec:ebl:ecbull:v:4:y:2003:i:38:p:1-10 is not listed on IDEAS
    6. Cocozza, R & Di Lorenzo, E & Sibillo, M, 2004. "Methodological problems in solvency assessment of an insurance company," MPRA Paper 27980, University Library of Munich, Germany.

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