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Title: Modeling the future development of IBNR and RBNS claims in the presence of covariates Authors:  Katrien Antonio - University of Amsterdam and KU Leuven (Belgium) [presenting]
Jonas Crevecoeur - KU Leuven (Belgium)
Roel Verbelen - KU Leuven (Belgium)
Abstract: Holding sufficient capital is essential for an insurance company to ensure its solvability. Predicting the amount of capital needed to fulfill future liabilities in an accurate way is an important actuarial task. Insurers record detailed information related to claims and policies for pricing insurance contracts. However, this same information is largely neglected when estimating the reserve. We present a flexible framework for including these claim specific covariates. Our framework focuses on three building blocks in the development process: the time to settlement, the number of payments and the size of each payment. We present a well-chosen generalized linear model (GLM) for each of these stochastic building blocks. Standard model selection techniques for GLMs allow us to determine the appropriate covariates in these models. We demonstrate how these covariates determine the granularity of our reserving model. On the one extreme, including many covariates, leads to large differences in the development process of individual claims. On the other extreme, including no covariates corresponds to specifying a model for data aggregated in a triangle. The set of selected covariates then naturally determines the position the actuary should take in between those two extremes.