Dependence Models for Actuarial Data.

点击翻译按钮获取中文摘要

When we fit a model to data, we are usually interested in representing the data the best way possible, and therefore in finding a model that fits the entire data set well. However, when the focus is on capturing the behaviour of extreme events - such as floods or large financial losses, for example - these models won't perform well. As a solution, extreme value methods can be applied to model only the data in the tail. But what about the situation where the non-extreme data are also of interest? When the data available concerns a single variable - for example, the modelling of the rainfall distribution at a particular location - there are statistical methods available that aim to accurately model the body of the distribution (i.e., data that aren't extreme) and the tail of the distribution (i.e., extreme events). However, when we have more than one variable - for example when an actuary is interested in modelling the dependence between liabilities in order to understand the exposure to risk - the situation is more complex, and sparse work has been done concerning the case where both extremes and the body are of interest. This project aims to fill this gap by investigating and developing dependence models which allow the tails to be considered appropriately, as well as accurately modelling the body of the data.In partnership with University College Dublin.