Nonparametric extreme value mixture models: applications to insurance losses

• Autor(a) principal: Galdino, Alexandre Bassi
• Data de Publicação: 2021
• Tipo de documento: Dissertação
• Idioma: eng
• Título da fonte: Repositório Institucional do FGV (FGV Repositório Digital)
• Texto Completo: https://hdl.handle.net/10438/30725
• topic: Insurance losses; Extreme value theory; Nonparametric methods; Kernel density; Finite mixture models; Severidade de sinistros; Teoria de valores extremos; Métodos não-paramétricos; Densidade Kernel; Modelos de mistura finita; Administração de empresas; Teoria dos valores extremos; Estatística não paramétrica; Sinistro (Seguros); Estatística - Análise

Modelling insurance losses is a challenging topic to actuaries and practitioners in the insurance industry. Commonly used loss models based on standard parametric density functions (Lognormal, Gamma, Weibull, Burr Type XII, Inverse Gaussian and Inverse Gamma) are often able to fit the bulk of the claim size distributions well but they fail to describe the behaviour of the most extremal observations. A popular approach used to overcome this limitation is to isolate the extreme data points and model them separately using Extreme Value Theory and the Generalized Pareto Distribution, an approach known as Peaks-Over-Threshold (POT) method. However, in most empirical applications, actuaries are interested in obtain a single model that provides a suitable global fit over the whole range of the distribution. In this thesis, we consider a nonparametric extreme value mixture model that is able to fit both small and large claims simultaneously. The model is extremely flexible due to its nonparametric component, avoiding the need to impose a functional form to the bulk of the loss distribution, as in most of the previous mixture approaches proposed in the actuarial literature. Further, the kernel density estimator has just a single extra parameter to be estimated, overcoming the problem of high computational burden related to other similar models. To illustrate the applicability and effectiveness of our model in the context of property and casualty losses, we consider three real data sets widely accessible and well-studied in the actuarial literature. The results suggest that the model provides a superior fit when compared with other existing alternatives.