Title: A general family of mixed exponential models applied to heavy-tailed losses
Authors: George Tzougas - London School of Economics and Political Science (United Kingdom) [presenting]
Dimitris Karlis - RC Athens University of Economics and Business (Greece)
Abstract: Regression modelling involving heavy-tailed response distributions, which have heavier tails than the exponential distribution, has become more and more popular in many insurance settings including non-life insurance. Mixed Exponential models can be considered as a natural choice for the distribution of heavy-tailed claim sizes since their tails are not exponentially bounded. However, apart from very few cases, such as the traditional Pareto regression model, this family of models has not been studied in depth. The main reason is that mixed Exponential models are not usually tractable because their likelihood is complicated and hence its maximization needs a special effort. The aim is to introduce a general family of mixed Exponential regression models with varying dispersion which can efficiently capture the tail behavior of losses. Our main achievement is that we present an Expectation-Maximization (EM) type algorithm which can facilitate maximum likelihood (ML) estimation for our class of mixed Exponential models which allows for regression specifications for both the mean and dispersion parameters. Finally, a real data application based on motor insurance data is given to illustrate the versatility of the proposed EM type algorithm.