Costruzione di Intervalli di Confidenza per le Stime del Premio per il Rischio nel Settore delle Assicurazioni Auto: Un Approccio basato sul Bootstrap

The motor insurance sector bases its foundation on advanced modeling techniques to estimate risk premiums, technical prices and tariffs. Each customer is appropriately analyzed in order to evaluate their probability of having claims and quantifying the possible losses. Each step of this process follows analytical statistical rules, each carefully studied and applied by specialists and experts in the motor insurance sector. This thesis explores how to use the bootstrap technique to build confidence intervals around these estimations, in particular for risk premiums in motor insurance technical pricing. The study centers on an in depth analysis of the motor sector of Generali Deutschland insurances, with a particular lens on its CosmosDirekt channel and Vollkasko policy. The risk premium estimation process is divided in several steps: first, it employs a weighted exponential Poisson Generalized Linear Model (GLM) targeting frequency, then it uses a gamma Generalized Linear Model (GLM) to encapsulate severity. The subsequent product of these models provides an estimate of the risk premium. The confidence intervals, obtained through a variant of the bootstrap technique devoid of replacement, are focused on several percentile ratios to compare the estimates. These intervals are instrumental in evaluating the accuracy of risk premium estimates, thereby offering insightful perspectives for informed risk management and decision-making practices within the motor insurance sector. A relevant portion of this elaborate also weights and examines the topic of a more balanced version of the sampling process during bootstrap cycles. The correct evaluation of a confidence interval for risk premium predictions is the first step towards a future possible analysis on technical premium and finally, leakage estimations.