The deductibles impact on the risk premium

Abstract: The aim of this master thesis is to derive methods that assesses the impact the deductiblehas on the risk premium of an insurance contract. The additive structure of a deductiblenecessitates approaches beyond treating it as a regular covariate in a generalized linearmodel for predicting the risk premium. Using simulated data, three methods areimplemented to estimate a parameter, denoted as βd ∈ [0,1], which quantifies the proportionof the risk premium that remains after imposing a deductible d on the insurance contract.The three implemented methods involve: 1) Regularized generalized linear models, 2)Utilizing the cumulative density function of the insurance contract, and 3) Estimating adiscrete probability distribution with K-means clustering and a classifier. To compare theperformance of these methods, they are tested against each other through a competition.The results reveal that the method employing the fitting of a discrete distribution yieldedthe best performance.