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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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    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. 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.
    4. 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.
    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. 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.
    7. 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.
    8. 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.

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