Jean-Philippe Boucher

Risk classification for claim counts: A comparative analysis of various zero-inflated mixed Poisson and hurdle models

Abstract This paper presents and compares different risk classification models for the annual number of claims reported to the insurer. Generalized heterogeneous, zero-inflated, hurdle, and compound frequency models are applied to a sample of an automobile portfolio of a major company operating in Spain. A statistical comparison between models is performed with the help of various specification tests (Score and Hausman tests for nested models, Vuong test or information criteria for nonnested ones). Interesting results about claiming behavior are obtained.

Fixed versus random effects in Poisson regression models for claim counts: a case study with motor insurance

This paper examines the validity of some stylized statements that can be found in the actuarial literature about random effects models. Specifically, the actual meaning of the estimated parameters and the nature of the residual heterogeneity are discussed. A numerical illustration performed on a Belgian motor third party liability portfolio supports this discussion.

A survey on models for panel count data with applications to insurance

In insurance the expected number of claims per year given the observed characteristics of the covered risk is the basis for setting the price of a policy. Companies accumulate information of clients along several years, but in practice the panel data structure is not exploited. We review panel count data models that are useful in this context and present a new alternative based on the generalization of a compound sum.ResumenEn seguros, el número esperado de reclamaciones por año dadas las características del riesgo cubierto es la base para establecer el precio de una póliza. Las compañías de seguros acumulan informaci ón de clientes a lo largo de varias anualidades, pero en la práctica la estructura de panel de los datos no se explota. Revisamos los modelos para paneles de datos de enumeración que son útiles en este contexto y presentamos una nueva alternativa basada en la generalización de una suma compuesta.

Multilevel modeling of insurance claims using copulas

In property and casualty insurance, claims management is featured with modeling of semicontinuous insurance cost associated with individual risk transfer. This practice is further complicated by the multilevel structure of the insurance claims data, where a contract often contains a group of policyholders, each policyholder is insured under multiple types of coverage, and the contract is repeatedly observed over time. The data hierarchy introduces complex dependence structure among claims and leads to diversification in the insurer’s liability portfolio. To capture the unique features of policy-level insurance costs, we propose a copula regression for the multivariate longitudinal claims. In the model, the Tweedie double generalized linear model is employed to examine the semi-continuous claim cost of each coverage type, and a Gaussian copula is specified to accommodate the cross-sectional and temporal dependence among the multilevel claims. Inference is based on the composite likelihood approach and the properties of parameter estimates are investigated through simulation. When applied to a portfolio of personal automobile policies from a Canadian insurer, we show that the proposed copula model provides valuable insights to an insurer’s claims management process.

A Semi-Nonparametric Approach to Model Panel Count Data

In count data models, overdispersion of the dependent variable can be incorporated into the model if a heterogeneity term is added into the mean parameter of the Poisson distribution. We use a nonparametric estimation for the heterogeneity density based on a squared Kth-order polynomial expansion, that we generalize for panel data. A numerical illustration using an insurance dataset is discussed. Even if some statistical analyses showed no clear differences between these new models and the standard Poisson with gamma random effects, we show that the choice of the random effects distribution has a significant influence for interpreting our results.

Sarmanov Family of Bivariate Distributions for Multivariate Loss Reserving Analysis

The correlation among multiple lines of business plays a critical role in aggregating claims and thus determining loss reserves for an insurance portfolio. We show that the Sarmanov family of bivariate distributions is a convenient choice to capture the dependencies introduced by various sources, including the common calendar year, accident year, and development period effects. The density of the bivariate Sarmanov distributions with different marginals can be expressed as a linear combination of products of independent marginal densities. This pseudo-conjugate property greatly reduces the complexity of posterior computations. In a case study, we analyze an insurance portfolio of personal and commercial auto lines from a major U.S. property-casualty insurer.

Frequency and Severity Modelling Using Multifractal Processes: An Application to Tornado Occurrence in the USA and CAT Bonds

This paper proposes a statistical model for insurance claims arising from climatic events, such as tornadoes in the USA, that exhibit a large variability both in frequency and intensity. To represent this variability and seasonality, the claims process modelled by a Poisson process of intensity equal to the product of a periodic function, and a multifractal process is proposed. The size of claims is modelled in a similar way, with gamma random variables. This method is shown to enable simulation of the peak times of damage. A two-dimensional multifractal model is also investigated. The work concludes with an analysis of the impact of the model on the yield of weather bonds linked to damage caused by tornadoes.

Modelling of Insurance Claim Count with Hurdle Distribution for Panel Data

The aim of the paper is to propose a new model for panel data. In a recent paper, the authors showed that the hurdle model is an interesting alternative to Poisson and Negative Binomial for the analysis of the number of claims reported by an insured driver. We generalize the hurdle model to account for longitudinal data under the assumption that covariates are time independent. Predictive distributions are shown to be easily computed analytically, as well as future premiums that can be calculated using the classical credibility theory.

Dynamic Moral Hazard: A Longitudinal Examination of Automobile Insurance in Canada: Dynamic Moral Hazard: A Longitudinal Examination of Automobile Insurance in Canada

This article examines moral hazard in the context of dynamic contracting in automobile insurance. Economic theory shows that experience rating of insurers results in state dependence of driving behavior under moral hazard. The empirical analysis is performed using a longitudinal data set from a Canadian automobile insurer. We employ dynamic nonlinear panel data models to distinguish the structural and spurious state dependence, and thus moral hazard and selection on unobservables. As a measure of the riskiness of driving, we consider the frequency, the number, as well as the cost of claims for the policyholder. We find that the state dependence in claim cost reflects both structural and spurious relationships, supporting the moral hazard hypothesis. However, the state dependence in claim occurrence is solely due to unobserved heterogeneity.