Sarmanov distribution for modeling dependence between the frequency and the severity of insurance claims

C. Bolancé Losilla, R. Vernic, R. Alemany Leira

In the classical collective model the random variable frequency is assumed to be independent of the random claim amounts. In practice, however, this independence assumption is often violated. In this paper, we analyze auto and home insurance claims. To model dependence in each insurance line, we assume that each random vector of frequency and severity follows a bivariate Sarmanov distribution. We present some properties of the resulting compound model and emphasize some particular cases. Furthermore, we analyze the dependence between both lines using a multivariate model with four distinct variables: two frequencies and two severities. We also aim to include covariates and use Generalised Linear Models (GLM) for marginals.
The maximum likelihood estimation of the parameters is also discussed. To illustrate the proposed models, we use a real data set of auto and home policies. Finally, effects on the premium are analyzed and new insurance pricing strategies are proposed.

Keywords: frequency-severity dependence, risk of claims, Sarnanov multivariate model, marginal GLMs

GT15-2 Risk Analysis
September 6, 2019  11:20 AM
I3L8. Georgina Blanes building

J. Pesantez-Narvaez, M. Alcañiz, M. Guillen

P. Ortega Jiménez, M. Á. Sordo Díaz, A. Suárez Llorens