Theoritical risk analysis in insurance using copulas

Abstract

This study develops credibility predictors of aggregate losses using NHIF data of the number of patients with same ailments in two different hospitals. For a model of aggregate losses, the interest is in predicting both the claim number process as well as the claim amount process. We consider a cross-section of risk classes with NHIF claims available for each risk class, this will help to explain and predict both the claim number and claim amount process. For marginal claims distributions this study uses generalized linear models, an extension of linear regression to describe cross-sectional characteristics. Copulas function is used to model the dependencies from the joint distribution functions and so separate out the dependence structure from the marginal distribution functions. The claim number process is represented using a poison regression model that is conditioned on sequence of variables, these variables drive the serial dependencies amount claims numbers, their joint distribution is represented using copula.