MackNet_Incurred: MackNet_Incurred

In EduardoRamosP/MackNet: Mack-Net model: Blending Mack's model with Recurrent Neural Networks

Description

It fits the incurred MackNet model. First, the ensemble of RNNs is fitted and the hyperparameters are optimized. Second, the predictive Mack parameters are computed taking into consideration the predictions made by the ensemble of RNNs. Third, bootstrapping is applied in order to produced a stochastic reserves distribution.

Usage

MackNet_Incurred(
  Cumulative.T,
  Incurred.T,
  Exposure,
  EarlyStoppingPatience = 50,
  Epochs = 1000,
  MinimumEpochs = 700,
  wd = 0,
  Learning = 0.01,
  drop = 0.1,
  Ensemble = 10,
  AR = 1,
  MackBias = 0,
  ZeroMean = 1,
  Control = 0,
  Simulations = 10000,
  Output = "relu"
)

Arguments

Cumulative.T	Cumulative payments triangle.
Incurred.T	Incurred cost triangle.
Exposure	Exposure measure. Written premiums is an appropriate measure to scale cumulative payments and incurred cost.
EarlyStoppingPatience	In case the error does not improve during the number of epochs defined by this variable, the training process stop and the weights are restored from the epoch with lower error. Default=300.
Epochs	Maximum number of epochs.
MinimumEpochs	Minimum number of epochs.
wd	The optimization algorithm used is ADAM. This variable defines the weighted decay.
Learning	Learning rate.
drop	Dropout regularization.
Ensemble	Number of RNNs included in the ensemble.
AR	This variable allows to remove the autorregressive component from the MackNet model when it is set to 0.
MackBias	If this variable is set to 0, the bias adjustment suggested by England y Verrall (2006) in "Predictive Distributions of Outstanding Liabilities in General Insurance" is applied, this means that residuals are multiplied by N/(N-p). In case this variable is set to 1, the adjustment suggested by Mack (1993) in "Distribution-free calculation of the standard error of chain ladder reserve estimates" is applied, this means that residuals are multiplied by n(i)/(n(i)-1). Finally, if this variable is set to 2, no adjustment is applied.
ZeroMean	If this variable is set to 0, residuals are not scaled to have zero mean. By default they are adjusted.
Control	Development factors below 0.975 are not allowed when this variable is set to 1.
Simulations	Number of triangle samples to be produced by the MackNet model.
Output	Linear or ReLU activation function for the output layer.

Value

The formula generates the following outputs:

• TestError Test error.

• Residuals MackNet residuals used during the bootrapping.

• Alpha Predective alpha parameter per development year. This parameters have a strong impact on the variance of the MackNet model.

• DevFactors Predective development factors per development year.

• SampledTriangles It contains all the triangles sampled by the MackNet model.

• SampledReserves It contains the total reserves sampled by the MackNet model.

• SampledReservesAY It contains the reserves by accident year sampled by the MackNet model.

• SampledUltimate It contains the total ultimates sampled by the MackNet model.

• SampledUltimateAY It contains the ultimates by accident year sampled by the MackNet model.

• EnsembleTriangles Triangles predicted by the ensemble of networks.

EduardoRamosP/MackNet documentation built on Sept. 26, 2020, 9:21 a.m.