Risk Model with Dependent Frequency and Severity, Premium and Ruin Probability Calculation

A common assumption made in classical risk theory with application in insurance modelling is that the "claim counts" and the "claim severity" are independent. It may not be the case in many situations. In recent times there have been authors working with models allowing some sort of dependence, good examples with application in motor insurance are Li et al. (2015),  Garrido et al. (2016) and Ni et al (2020). Also, we mention Albrecher et al (2011), Andrade e Silva (2017) and Moura e Centeno (2020). They use different methods to capture dependence, eg. the first and last  use copulae and the second uses GLM.

By using using real data from two different, but related, branches on housing and liability insurance from an anonymous insurer, we work numerical illustrations. We consider dependence between claim counts and severity of claims, as well as among individual claims  in order to estimate subsequent premiums and corresponding ruin probabilities. 

We work formulae and numerical results for both ruin probabilities and adjusted premiums in some sort of models. We start from studying two separate compound Poisson models and study existence of dependence, then its size using appropriate methods, either copulae, regression or mixing Poisson parametrization. Our database has the novelty of not coming from automobile insurance, thus bringing other challenges.