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Emiliano A. Valdez:Joint Modeling of Customer Loyalty and Risk in Personal Insurance


Time: 2021/5/13 9:00-10:00 AM

Form:Tencent Meeting (ID:705 456 950)

Topic:Joint Modeling of Customer Loyalty and Risk in Personal Insurance


This work connects two strands of research of modeling personal (automobile and homeowners) insurance. One strand involves understanding the joint outcomes of separate personal insurance contracts, e.g., do higher automobile claims suggest more severe homeowner claims? Joint modeling of personal insurance is complicated by the fact that the outcomes typically have a mass at zero, corresponding to no claims, and when there are claims, distributions tend to be right-skewed and long-tailed. Moreover, it is important to account for insured personal characteristics as well as characteristics of the contract and, in the case of auto and homeowners, features of the automobile and the house. A second strand of the literature involves understanding determinants of customer loyalty. For example, we now know that when a customer cancels one insurance contract, he or she is likely to cancel all other contracts soon after.

This paper examines longitudinal data from a major Spanish insurance company that offers automobile and homeowners insurance. The dataset tracks 890,542 clients over five years, many of whom subscribed to both automobile and homeowners insurance (75,536, or approximately 8.5%). To represent this data, we use copula regression to model the joint outcomes of auto and home claims as well as customer loyalty. Including customer loyalty, or duration with the company, is complicated because of the censoring of this time variable as well as the discreteness. Although customers may cancel the contract at any time, cancelation typically occurs at contract renewal, making this variable essentially a discrete outcome. Composite likelihood and generalized method of moments techniques allow us to address the special features of this data structure. Our estimation results provide evidence of interesting relationships among auto claims, home claims and customer loyalty.

Consistent with findings from other studies, we find that intertemporal dependencies are important, e.g., high auto claims from one year signal high auto claims for the following year. Work is ongoing to develop strategies that will allow the insurance manager to identify profitable portfolios through measurement of a customer loyalty index.

A link to a related work is

Keywords: copula regression, logistic regression, Tweedie regression, generalized method of moments (GMM), insurance pricing.


Emil is a Fellow of the Society of Actuaries and holds a Ph.D. from the University of Wisconsin in Madison. His most recent post was at Michigan State University in East Lansing as professor and director of their actuarial science program. His primary research interest is actuarial science that cover topics in copula models and dependencies, applications of statistics to insurance problems, managing post-retirement assets, and risk measures and capital requirements related to enterprise risk management. In recognition for the quality of his research, he has been awarded several prizes that include the E. A. Lew Award, the Halmstad Memorial Prize, and the Hachemeister Prize. Emil also has a joint appointment at the Department of Statistics at the University of Connecticut.

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