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Detecting fuzzy relationships in regression models: The case of insurer solvency surveillance in Germany

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  • Berry-Stölzle, Thomas R.
  • Koissi, Marie-Claire
  • Shapiro, Arnold F.

Abstract

We develop a test for the fuzziness of regression coefficients based on the Tanaka et al. (1982) and He et al. (2007) possibilistic fuzzy regression models. We interpret the spread of the regression coefficients as a statistic measuring the fuzziness of the relationship between the corresponding independent variable and the dependent variable. We derive test distributions based on the null hypothesis that such spreads could have been obtained by estimating a possibilistic regression with data generated by a classical regression model with random errors. As an example, we show how our test detects a fuzzy regression coefficient in a solvency prediction model for German property-liability insurance companies.

Suggested Citation

  • Berry-Stölzle, Thomas R. & Koissi, Marie-Claire & Shapiro, Arnold F., 2010. "Detecting fuzzy relationships in regression models: The case of insurer solvency surveillance in Germany," Insurance: Mathematics and Economics, Elsevier, vol. 46(3), pages 554-567, June.
  • Handle: RePEc:eee:insuma:v:46:y:2010:i:3:p:554-567
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    References listed on IDEAS

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    1. Lemaire, Jean, 1990. "Fuzzy Insurance," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 20(01), pages 33-55, April.
    2. J. David Cummins & Martin F. Grace & Richard D. Phillips, 1998. "Regulatory solvency prediction in property-liability insurance: risk-based capital, audit ratios, and cash flow simulation," Working Papers 98-20, Federal Reserve Bank of Philadelphia.
    3. Lamm-Tennant, Joan & Starks, Laura T, 1993. "Stock versus Mutual Ownership Structures: The Risk Implications," The Journal of Business, University of Chicago Press, vol. 66(1), pages 29-46, January.
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    5. Shapiro, Arnold F., 2004. "Fuzzy logic in insurance," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 399-424, October.
    6. Jorge de Andrés Sánchez & Antonio Terceño Gómez, 2003. "Applications of Fuzzy Regression in Actuarial Analysis," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 70(4), pages 665-699.
    7. J. Cummins & Gregory Nini, 2002. "Optimal Capital Utilization by Financial Firms: Evidence from the Property-Liability Insurance Industry," Journal of Financial Services Research, Springer;Western Finance Association, vol. 21(1), pages 15-53, February.
    8. Ian G. Sharpe & Andrei Stadnik, 2007. "Financial Distress in Australian General Insurers," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 74(2), pages 377-399.
    9. Steven Pottier & David Sommer, 2002. "The Effectiveness of Public and Private Sector Summary Risk Measures in Predicting Insurer Insolvencies," Journal of Financial Services Research, Springer;Western Finance Association, vol. 21(1), pages 101-116, February.
    10. He, Yan-Qun & Chan, Lai-Kow & Wu, Ming-Lu, 2007. "Balancing productivity and consumer satisfaction for profitability: Statistical and fuzzy regression analysis," European Journal of Operational Research, Elsevier, vol. 176(1), pages 252-263, January.
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    Citations

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    Cited by:

    1. Rachida Hennani & Michel Terraza, 2012. "Value-at-Risk stressée chaotique d’un portefeuille bancaire," Working Papers 12-23, LAMETA, Universitiy of Montpellier, revised Sep 2012.
    2. Sadefo Kamdem, J. & Mbairadjim Moussa, A. & Terraza, M., 2012. "Fuzzy risk adjusted performance measures: Application to hedge funds," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 702-712.
    3. Mbairadjim Moussa, A. & Sadefo Kamdem, J. & Shapiro, A.F. & Terraza, M., 2014. "CAPM with fuzzy returns and hypothesis testing," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 40-57.

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