Title: Insurance ratemaking using the exponential-lognormal regression model
Authors: George Tzougas - London School of Economics and Political Science (United Kingdom)
Muhammad Waqar Mustaqeem - London School of Economics and Political Science (United Kingdom)
Woo Hee Yik - London school of economics and political science (United Kingdom) [presenting]
Abstract: The exponential-lognormal regression model is introduced as an alternative to the Pareto regression model that has been widely used for modelling the cost of claims as a function of their risk characteristics in an abundance of alternative insurance applications. The exponential-lognormal regression model can be considered as a plausible model for approximating moderate claim costs which are more frequent than large claim sizes when dealing with real insurance data sets. However, this is the first time that it is used in a statistical or an actuarial context because its log-likelihood is complicated, and hence its maximization needs a special effort. The main contribution is to illustrate that ML estimation of the exponential-lognormal regression model can be accomplished relatively easily via an expectation maximization (EM) algorithm which can address situations where the mixing distribution, such as the lognormal, is not conjugate to the exponential distribution. A real data application based on motor insurance data is examined in order to illustrate the versatility of the proposed algorithm. Finally, assuming that the number of claims follows the negative binomial model, both the a priori and a posteriori premium rates resulting from the exponential-lognormal model for approximating claim sizes are calculated via the net premium principle and compared to those determined by the Pareto model, that has been traditionally used for modelling losses.