Enhanced Insurance Risk Assessment using Discrete Four-Variate Sarmanov Distributions and Generalized Linear Models

Abstract

This research paper investigated multivariate risk assessment in insurance, focusing on four risks of a singular person and their interdependence. This research examined various risk indicators in non-life insurance which was under-writing for organizations with clients that purchase several non-life insurance policies. The risk indicators are probabilities of frequency claims and correlations of two risk lines. The closed forms of probability mass functions evaluated the probabilities of frequency claims. Three generalized linear models of four-variate Sarmanov distributions were proposed for marginals, incorporating various characteristics of policyholders using explanatory variables. All three models were discrete models that were a combination of Poisson and Gamma distributions. Some properties of four-variate Sarmanov distributions were explicitly shown in closed forms. The dataset spanned a decade and included the exposure of each individual to risk over an extended period. The correlations between the two risk types were evaluated in several statistical ways. The parameters of the three Sarmanov model distributions were estimated using the maximum likelihood method, while the results of the three models were compared with a simpler four-variate negative binomial generalized linear model. The research findings showed that Model 3 was the most accurate of all three models since the AIC and BIC were the lowest. In terms of the correlation, it was found that the risk of claiming auto insurances was related to claiming home insurances. Model 1 could be used for the risk assessment of an insurance company that had customers who held multiple types of insurances in order to predict the risks that may occur in the future. When the insurance company can forecast the risks that may occur in the future, the company will be able to calculate appropriate insurance premiums.