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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. 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.
    2. Andre P. Liebenberg & David W. Sommer, 2008. "Effects of Corporate Diversification: Evidence From the Property–Liability Insurance Industry," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 75(4), pages 893-919, December.
    3. 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, December.
    4. 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.
    5. Lemaire, Jean, 1990. "Fuzzy Insurance," ASTIN Bulletin, Cambridge University Press, vol. 20(1), pages 33-55, April.
    6. Cummins, J. David & Harrington, Scott E. & Klein, Robert, 1995. "Insolvency experience, risk-based capital, and prompt corrective action in property-liability insurance," Journal of Banking & Finance, Elsevier, vol. 19(3-4), pages 511-527, June.
    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, June.
    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. Renbao Chen & Kie Ann Wong, 2004. "The Determinants of Financial Health of Asian Insurance Companies," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 71(3), pages 469-499, September.
    11. 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.
    12. Shapiro, Arnold F., 2004. "Fuzzy logic in insurance," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 399-424, October.
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    Cited by:

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    2. Jelena Lukić & Mirjana Misita & Dragan D. Milanović & Ankica Borota-Tišma & Aleksandra Janković, 2022. "Determining the Risk Level in Client Analysis by Applying Fuzzy Logic in Insurance Sector," Mathematics, MDPI, vol. 10(18), pages 1-17, September.
    3. 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.
    4. Alfred Mbairadjim Moussa & Jules Sadefo Kamdem, 2022. "A fuzzy multifactor asset pricing model," Annals of Operations Research, Springer, vol. 313(2), pages 1221-1241, June.
    5. 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.
    6. Ignacio Moreno & Purificación Parrado‐Martínez & Antonio Trujillo‐Ponce, 2020. "Economic crisis and determinants of solvency in the insurance sector: new evidence from Spain," Accounting and Finance, Accounting and Finance Association of Australia and New Zealand, vol. 60(3), pages 2965-2994, September.
    7. Rachida Hennani & Michel Terraza, 2012. "Value-at-Risk stressée chaotique d’un portefeuille bancaire," Working Papers 12-23, LAMETA, Universtiy of Montpellier, revised Sep 2012.
    8. Muhammed Altuntas & Gerrit Gößmann, 2016. "The Relationship Between Home Market Performance and Internationalization Decisions: Evidence From German Insurance Groups," Risk Management and Insurance Review, American Risk and Insurance Association, vol. 19(1), pages 37-71, March.

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