Titolo della tesi: Advances in Claims Reserve Modelling
In the non-life insurance industry, insurance companies are required by local and international regulators to set aside an amount, known as the claims reserve, to meet future payment obligations. The market data shows that the claims reserve represents the main liability of non-life (re)insurance companies (EIOPA, 2023), and we refer to its calculation at a valuation date as reserving. From a statistical perspective, this is a prediction problem. For reserving, the industry relies on simple algorithms that use an aggregated data representation called development triangles. The more detailed databases that make up the development triangles are often held by insurers and contain information about claims at an individual level that could potentially improve reserving. Examples are static covariates like age and insurance type, accident times, payment delays or payment costs.
When the reserve is computed, the data is only partially observed due to so-called right-censoring. At this point, not all the claim histories are observed, so that for some it is only known that payments might occurr in the future; this context of incomplete information makes the statistical models for event history analysis a natural framework for dealing with this type of application.
The purpose of this monograph is to illustrate three models for reserving based on the outlined framework. Our problem formulation allows us to deal with incomplete observations of claims data and to incorporate information on individual covariates. By applying our models to both simulated and real data sets, and comparing them with approaches based on development triangles, we find that these sophisticated models allow for more accurate estimates of the claims reserve.