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Insurance Ratemaking and a Gini Index

Author

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  • Edward W. (Jed) Frees
  • Glenn Meyers
  • A. David Cummings

Abstract

type="main" xml:lang="en"> Welfare economics uses Lorenz curves to display skewed income distributions and Gini indices to summarize the skewness. This article extends the Lorenz curve and Gini index by ordering insurance risks; the ordering variable is a risk-based score relative to price, known as a relativity. The new relativity-based measures can cope with adverse selection and quantify potential profit. Specifically, we show that the Gini index is proportional to a correlation between the relativity and an out-of-sample profit (price in excess of loss). A detailed example using homeowners insurance demonstrates the utility of these new measures.

Suggested Citation

  • Edward W. (Jed) Frees & Glenn Meyers & A. David Cummings, 2014. "Insurance Ratemaking and a Gini Index," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 81(2), pages 335-366, June.
    • Handle: RePEc:bla:jrinsu:v:81:y:2014:i:2:p:335-366
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    Cited by:

    1. Devriendt, Sander & Antonio, Katrien & Reynkens, Tom & Verbelen, Roel, 2021. "Sparse regression with Multi-type Regularized Feature modeling," Insurance: Mathematics and Economics, Elsevier, vol. 96(C), pages 248-261.
    2. Denuit, Michel & Trufin, Julien & Verdebout, Thomas, 2021. "Testing for more positive expectation dependence with application to model comparison," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 163-172.
    3. Martin Eling & Ruo Jia, 2017. "Recent Research Developments Affecting Nonlife Insurance—The CAS Risk Premium Project 2014 Update," Risk Management and Insurance Review, American Risk and Insurance Association, vol. 20(1), pages 63-77, March.
    4. Barry C. Arnold & José María Sarabia, 2018. "Analytic Expressions for Multivariate Lorenz Surfaces," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(1), pages 84-111, December.
    5. Deprez, Laurens & Antonio, Katrien & Boute, Robert, 2023. "Empirical risk assessment of maintenance costs under full-service contracts," European Journal of Operational Research, Elsevier, vol. 304(2), pages 476-493.
    6. Chenglong Ye & Lin Zhang & Mingxuan Han & Yanjia Yu & Bingxin Zhao & Yuhong Yang, 2022. "Combining Predictions of Auto Insurance Claims," Econometrics, MDPI, vol. 10(2), pages 1-15, April.
    7. Meng, Shengwang & Gao, Yaqian & Huang, Yifan, 2022. "Actuarial intelligence in auto insurance: Claim frequency modeling with driving behavior features and improved boosted trees," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 115-127.
    8. Deprez, Laurens & Antonio, Katrien & Boute, Robert, 2021. "Pricing service maintenance contracts using predictive analytics," European Journal of Operational Research, Elsevier, vol. 290(2), pages 530-545.
    9. Giovanni Maria Giorgi, 2019. "The Gini concentration ratio: Back to the future," RIEDS - Rivista Italiana di Economia, Demografia e Statistica - The Italian Journal of Economic, Demographic and Statistical Studies, SIEDS Societa' Italiana di Economia Demografia e Statistica, vol. 73(2), pages 5-14, April-Jun.
    10. Samanthi, Ranadeera Gamage Madhuka & Wei, Wei & Brazauskas, Vytaras, 2016. "Ordering Gini indexes of multivariate elliptical risks," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 84-91.
    11. Xiaoshan Su & Manying Bai, 2020. "Stochastic gradient boosting frequency-severity model of insurance claims," PLOS ONE, Public Library of Science, vol. 15(8), pages 1-24, August.
    12. Li, Zhengxiao & Wang, Fei & Zhao, Zhengtang, 2024. "A new class of composite GBII regression models with varying threshold for modeling heavy-tailed data," Insurance: Mathematics and Economics, Elsevier, vol. 117(C), pages 45-66.
    13. Cheung, Eric C.K. & Ni, Weihong & Oh, Rosy & Woo, Jae-Kyung, 2021. "Bayesian credibility under a bivariate prior on the frequency and the severity of claims," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 274-295.
    14. Giovanni M. Giorgi & Stefania Gubbiotti, 2017. "Celebrating the Memory of Corrado Gini: a Personality Out of the Ordinary," International Statistical Review, International Statistical Institute, vol. 85(2), pages 325-339, August.
    15. Jeong, Himchan & Valdez, Emiliano A., 2020. "Predictive compound risk models with dependence," Insurance: Mathematics and Economics, Elsevier, vol. 94(C), pages 182-195.
    16. Oh, Rosy & Jeong, Himchan & Ahn, Jae Youn & Valdez, Emiliano A., 2021. "A multi-year microlevel collective risk model," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 309-328.
    17. Denuit, Michel & Trufin, Julien & Verdebout, Thomas, 2021. "Testing for more positive expectation dependence with application to model comparison," LIDAM Discussion Papers ISBA 2021021, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    18. Pavkova, Katerina & Currie, Graham & Delbosc, Alexa & Sarvi, Majid, 2016. "Selecting tram links for priority treatments - The Lorenz Curve approach," Journal of Transport Geography, Elsevier, vol. 55(C), pages 101-109.
    19. Luigi Biagini & Simone Severini, 2021. "The role of Common Agricultural Policy (CAP) in enhancing and stabilising farm income: an analysis of income transfer efficiency and the Income Stabilisation Tool," Papers 2104.14188, arXiv.org.
    20. Chuancun Yin, 2019. "Stochastic ordering of Gini indexes for multivariate elliptical random variables," Papers 1908.01943, arXiv.org, revised Sep 2019.

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