Abstract
The goal of this paper is to develop regression models and postulate distributions which can be used in practice to describe the joint development process of individual claim payments and claim incurred. We apply neural networks to estimate our regression models. As regressors we use the whole claim history of incremental payments and claim incurred, as well as any relevant feature information which is available to describe individual claims and their development characteristics. Our models are calibrated and tested on a real data set, and the results are benchmarked with the Chain-Ladder method. Our analysis focuses on the development of the so-called Reported But Not Settled (RBNS) claims. We show benefits of using deep neural network and the whole claim history in our prediction problem.
Highlights
Stochastic models for individual claims reserving were introduced roughly 30 years ago in the work of (Arjas 1989) and (Norberg 1993 1999)
We develop regression models and postulate distributions which can be used in practice to describe the joint development process of individual claim payments and claim incurred
We recommend to use the Combined Actuarial Neural Network (CANN) approach of (Schelldorfer and Wüthrich 2019)—we suggest to use generalized linear models (GLMs), generalized additive models (GAMs) or regression trees as initial predictions, or as the initial models, from which we start training the neural networks
Summary
Stochastic models for individual claims reserving were introduced roughly 30 years ago in the work of (Arjas 1989) and (Norberg 1993 1999). We develop regression models and postulate distributions which can be used in practice to describe the joint development process of individual claim payments and claim incurred. We use multinomial/binomial cross-entropy and Gamma loss functions for calibrations of our neural networks These loss functions are related to the distributions of the variables which we would like to use for predictions in the claim development process. To the best of our knowledge this is the first paper in insurance data science where outstanding liabilities are predicted with neural networks and compared with classical chain-ladder estimates. This comparison on a real data set is the fifth contribution of this paper. All calculations were done in Keras, which is an open-source API to TensorFlow
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