C40 - Econometric and Statistical Methods: Special Topics: GeneralReturn

This article outlines possibilities of modeling the distribution of the future liabilities of an insurance company that stem from a past claim which has not yet been settled. Such a model might be used as a key component of the internal model of the reserve risk of an insurance company. It focuses on a probabilistic description of the settlement process of an individual loss, i.e., on the development of the incurred value over the lifetime of the loss. Such a model allows setting up an internal model based on an individual claim level instead of the aggregate claim level common nowadays. The proposed model respects two main restrictions given by potential industrial usage: Firstly, the model is set up in such a way that necessary data can be assumed to be available from a practical point of view. Besides that, potential requirements on the complexity of the model are considered and simplifying assumptions that allow setting up a model with 'reasonable complexity' for practical use are suggested and commented on from a practical point of view.
Calibration of the model of changes in the anticipated loss (more precisely, the incurred value changes) is illustrated on real data (adjusted for confidentiality purposes). The joint modeling procedure is applied, where a generalized linear model is assumed as a model of the incurred value (response variable) as well as its response variance. Interesting properties which might be expected in similar portfolios are revealed in the data.