Joint Models of Insurance Lapsation and Claims
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This paper introduces a generalized method of moments technique to estimate dependence parameters in a multivariate copula regression framework. This framework is motivated by insurance applications, where it is common to have outcomes, such as insurance claims, that may be from a discrete, a long-tailed continuous, or a hybrid combination of discrete and continuous distributions. Copula methods are natural for modeling dependence when the outcome distribution may be complicated especially in the presence of covariates. The paper also considers extensions to handle insurance lapsation. In the insurance context, claims outcomes may be related to a policyholder's decision to lapse (or the converse, renew) a policy. Motivated by insurance, this paper introduces a copula model where longitudinal outcomes may be related to lapsation, a time-to-event random variable, that accounts for this dependence. A simulation study demonstrates the viability of the approach. Also considered is a sample from a Spanish insurer that includes auto and homeowners claims. The paper describes how the joint model provides new information that insurers can use to better manage their portfolios of risks.
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