The purpose of this project is to present a claims reserving technique that uses claim-specific feature and past payment information in order to estimate claims reserves for individual reported claims. We design a single neural network for this task. It models the expected payments in all considered payment delay periods on the basis of claim-specific feature and past payment information, separately for every individual reported claim. This single neural network consists of several subnets. Every subnet serves the purpose of modeling the expected payment in the corresponding payment delay period. The separate subnets allow for sufficient flexibility to jointly model all considered payment delay periods in one neural network. However, the subnets are still connected to each other by sharing some of the neural network parameters. This increases stability of the neural network, and allows us to learn from one payment delay period to the other.
A key problem of individual claims reserving models is the incomplete time series structure of past payments. Individual claims are equipped with different amounts of past payment information, depending on the reporting years of the claims. This problem is addressed by combining embedding layers and dropout layers. We assume that expected future payments depend on past payments only through the order of magnitude of these payments. We then introduce the additional label “no information” for past payments variables, and set the neural network embedding weights for this label to zero. This does not result in a loss of generality, as there are no restrictions for the other labels. By applying dropout layers on past payment information during neural network fitting, i.e. by randomly setting some of the corresponding neurons to zero, we mimic the situation of missing parts of the past payment information. This forces the neural network to learn how to cope with the situation of only knowing parts of the past payment information.
In this project we work with a synthetic insurance dataset generated by an individual claims history simulation machine. This synthetic dataset consists of individual claims from six lines of business for which we have complete information. We remark that having complete information is crucial for this project, as it allows us to back-test the newly developed claims reserving model for reported claims.
The R code for applying the neural network individual RBNS claims reserving model is provided in the zip file NeuralNetworkIndividualClaimsReservingGitHub.zip. The zip file contains seven R codes: The file DataGeneration.R describes the generation of the synthetic data.
The file NeuralNetworkModels.R provides the neural network model.
The file EmbeddingWeights.R performs the first training step which determines the embedding weights.
The file NeuralNetworkWeights.R performs the second training step which determines the remaining neural network weights.
The file VarianceParameters.R is used to estimate the variance parameters of the log-normal distributions.
The file Recoveries.R estimates the recovery payments.
The file RBNSReserves.R calculates the individual RBNS claims reserves.
Moreover, it contains 3 folders: The folder SimulationMachine contains the individual claims history simulation machine needed for generating the data.
The folder Data contains the generated data.
The folder Results contains the results of the individual RBNS claims reserving.
For the theoretical details we refer to the corresponding paper.