Bayesian insurance pricing using informative prior estimation techniques

Abstract: Large, well-established insurance companies build statistical pricing models based on customer claim data. Due to their long experience and large amounts of data, they can predict their future expected claim losses accurately. In contrast, small newly formed insurance start-ups do not have access to such data. Instead, a start-up’s pricing model’s initial parameters can be set by directly estimating the risk premium tariff’s parameters in a non-statistical manner. However, this approach results in a pricing model that cannot be adjusted based on new claim data through classical frequentist insurance approaches. This thesis has put forth three Bayesian approaches for including estimates of an existing multiplicative tariff as the expectation of a prior in a Generalized Linear Model (GLM). The similarity between premiums set using the prior estimations and the static pricing model was measured as their relative difference. The results showed that the static tariff could be closely estimated. The estimated priors were then merged with claim data through the likelihood. These posteriors were estimated via the two Markov Chain Monte Carlo approaches, Metropolis and Metropolis-Hastings. All in all, this resulted in three risk premium models that could take advantage of existing pricing knowledge and learn over time as new cases arrived. The results showed that the Bayesian pricing methods significantly reduced the discrepancy between predicted and actual claim costs on an overall portfolio level compared to the static tariff. Nevertheless, this could not be determined on an individual policyholder level.