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Knowledge Learning of Insurance Risks Using Dependence Models

Author

Listed:
  • Zifeng Zhao

    (Department of Information Technology, Analytics, and Operations, Mendoza College of Business, University of Notre Dame, Notre Dame, Indiana 46556)

  • Peng Shi

    (Risk and Insurance Department, Wisconsin School of Business, University of Wisconsin-Madison, Madison, Wisconsin 53706)

  • Xiaoping Feng

    (CapitalG, Mountain View, California 94043)

Abstract

Learning the customers’ experience and behavior creates competitive advantages for any company over its rivals. The insurance industry is an essential sector in any developed economy and a better understanding of customers’ risk profile is critical to decision making in all aspects of insurance operations. In this paper, we explore the idea of using copula-based dependence models to learn the hidden risk of policyholders in property insurance. Specifically, we build a novel copula model to accommodate the dependence over time and over space among spatially clustered property risks. To tackle the computational challenge caused by the discreteness feature of large-scale insurance data, we propose an efficient multilevel composite likelihood approach for parameter estimation. Provided that latent risk induces correlation, the proposed customer learning method offers improved predictive analytics by allowing insurers to borrow strength from related risks in predicting new risks and also helps reveal the relative importance of the multiple sources of unobserved heterogeneity in updating policyholders’ risk profile. In the empirical study, we examine the loss cost of a portfolio of entities insured by a government property insurance program in Wisconsin. We find both significant temporal and spatial association among property risks. However, their effects on the predictive distribution of loss cost are different for the new and renewal policyholders. The two sources of dependence are complements for the former and substitutes for the latter. These findings are shown to have substantial managerial implications in key insurance operations such as experience rating, capital allocation, and reinsurance arrangement.

Suggested Citation

  • Zifeng Zhao & Peng Shi & Xiaoping Feng, 2021. "Knowledge Learning of Insurance Risks Using Dependence Models," INFORMS Journal on Computing, INFORMS, vol. 33(3), pages 1177-1196, July.
  • Handle: RePEc:inm:orijoc:v:33:y:2021:i:3:p:1177-1196
    DOI: 10.1287/ijoc.2020.1005
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    1. Peter Guttorp & Tilmann Gneiting, 2006. "Studies in the history of probability and statistics XLIX On the Matern correlation family," Biometrika, Biometrika Trust, vol. 93(4), pages 989-995, December.
    2. Mullahy, John, 1998. "Much ado about two: reconsidering retransformation and the two-part model in health econometrics," Journal of Health Economics, Elsevier, vol. 17(3), pages 247-281, June.
    3. John Mullahy, 1998. "Much Ado About Two: Reconsidering Retransformation and the Two-Part Model in Health Economics," NBER Technical Working Papers 0228, National Bureau of Economic Research, Inc.
    4. Frees, Edward W. & Shi, Peng & Valdez, Emiliano A., 2009. "Actuarial Applications of a Hierarchical Insurance Claims Model," ASTIN Bulletin, Cambridge University Press, vol. 39(1), pages 165-197, May.
    5. Frees, Edward W. & Meyers, Glenn & Cummings, A. David, 2011. "Summarizing Insurance Scores Using a Gini Index," Journal of the American Statistical Association, American Statistical Association, vol. 106(495), pages 1085-1098.
    6. Alma Cohen, 2012. "Asymmetric Learning in Repeated Contracting: An Empirical Study," The Review of Economics and Statistics, MIT Press, vol. 94(2), pages 419-432, May.
    7. Smyth, Gordon K. & Jørgensen, Bent, 2002. "Fitting Tweedie's Compound Poisson Model to Insurance Claims Data: Dispersion Modelling," ASTIN Bulletin, Cambridge University Press, vol. 32(1), pages 143-157, May.
    8. Levon Barseghyan & Francesca Molinari & Darcy Steeg Morris & Joshua C. Teitelbaum, 2020. "The Cost of Legal Restrictions on Experience Rating," Journal of Empirical Legal Studies, John Wiley & Sons, vol. 17(1), pages 38-70, March.
    9. Peng Shi & Wei Zhang, 2016. "A Test of Asymmetric Learning in Competitive Insurance With Partial Information Sharing," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 83(3), pages 557-578, September.
    10. Yanwei Zhang & Vanja Dukic, 2013. "Predicting Multivariate Insurance Loss Payments Under the Bayesian Copula Framework," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 80(4), pages 891-919, December.
    11. Bahar Biller, 2009. "Copula-Based Multivariate Input Models for Stochastic Simulation," Operations Research, INFORMS, vol. 57(4), pages 878-892, August.
    12. Peng Shi & Lu Yang, 2018. "Pair Copula Constructions for Insurance Experience Rating," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(521), pages 122-133, January.
    13. Peng Shi, 2016. "Insurance ratemaking using a copula-based multivariate Tweedie model," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2016(3), pages 198-215, March.
    14. Krämer, Nicole & Brechmann, Eike C. & Silvestrini, Daniel & Czado, Claudia, 2013. "Total loss estimation using copula-based regression models," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 829-839.
    15. Cristiano Varin & Paolo Vidoni, 2005. "A note on composite likelihood inference and model selection," Biometrika, Biometrika Trust, vol. 92(3), pages 519-528, September.
    16. Joe, Harry & Lee, Youngjo, 2009. "On weighting of bivariate margins in pairwise likelihood," Journal of Multivariate Analysis, Elsevier, vol. 100(4), pages 670-685, April.
    17. Yun Bai & Peter X.-K. Song & T. E. Raghunathan, 2012. "Joint composite estimating functions in spatiotemporal models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 74(5), pages 799-824, November.
    18. Yun Bai & Jian Kang & Peter X.-K. Song, 2014. "Efficient pairwise composite likelihood estimation for spatial-clustered data," Biometrics, The International Biometric Society, vol. 70(3), pages 661-670, September.
    19. Edward Frees & Emiliano Valdez, 1998. "Understanding Relationships Using Copulas," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(1), pages 1-25.
    20. Mercedes Ayuso & Montserrat Guillen & Jens Perch Nielsen, 2019. "Improving automobile insurance ratemaking using telematics: incorporating mileage and driver behaviour data," Transportation, Springer, vol. 46(3), pages 735-752, June.
    21. Lemaire, Jean, 1984. "An Application of Game Theory: Cost Allocation," ASTIN Bulletin, Cambridge University Press, vol. 14(1), pages 61-81, April.
    22. Edward W. Frees, 2015. "Analytics of Insurance Markets," Annual Review of Financial Economics, Annual Reviews, vol. 7(1), pages 253-277, December.
    23. Pavel Krupskii & Raphaël Huser & Marc G. Genton, 2018. "Factor Copula Models for Replicated Spatial Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(521), pages 467-479, January.
    24. Moreno Bevilacqua & Carlo Gaetan & Jorge Mateu & Emilio Porcu, 2012. "Estimating Space and Space-Time Covariance Functions for Large Data Sets: A Weighted Composite Likelihood Approach," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(497), pages 268-280, March.
    25. Bahar Biller & Canan G. Corlu, 2011. "Accounting for Parameter Uncertainty in Large-Scale Stochastic Simulations with Correlated Inputs," Operations Research, INFORMS, vol. 59(3), pages 661-673, June.
    26. Seokho Lee & Marc G. Genton & Reinaldo B. Arellano-Valle, 2010. "Perturbation of Numerical Confidential Data via Skew-t Distributions," Management Science, INFORMS, vol. 56(2), pages 318-333, February.
    27. Ali E. Abbas, 2013. "Utility Copula Functions Matching All Boundary Assessments," Operations Research, INFORMS, vol. 61(2), pages 359-371, April.
    28. Lemaire, Jean, 1991. "Cooperative Game Theory and its Insurance Applications," ASTIN Bulletin, Cambridge University Press, vol. 21(1), pages 17-40, April.
    29. Kunreuther, Howard & Pauly, Mark, 1985. "Market equilibrium with private knowledge : An insurance example," Journal of Public Economics, Elsevier, vol. 26(3), pages 269-288, April.
    30. Frees, Edward W. & Wang, Ping, 2006. "Copula credibility for aggregate loss models," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 360-373, April.
    31. Frees, Edward W. (Jed) & Meyers, Glenn & Cummings, A. David, 2010. "Dependent Multi-Peril Ratemaking Models," ASTIN Bulletin, Cambridge University Press, vol. 40(2), pages 699-726, November.
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