DeepTriangle: A Deep Learning Approach to Loss Reserving

This is the companion repository to the DeepTriangle paper. A preprint can be found at https://arxiv.org/abs/1804.09253.

Reproducing experiments

Note: Due to changes in some library dependencies over time, the results may not reproduce exactly depending on when you installed TensorFlow, but the conclusions of the paper remain unchanged. The results below are generated using TensorFlow 1.10 and Keras 2.2.

To get started, either clone the repo and build the R package, or install with

devtools::install_github("kevinykuo/deeptriangle")

You will also need the insurance package, which can be installed with

devtools::install_github("kevinykuo/insurance")

The following lines of code will instantiate and fit the model for each line of business then combine the forecasts in a data frame:

library(deeptriangle)
library(tidyverse)
library(keras)

use_implementation("tensorflow")

# set seed for reproducibility
use_session_with_seed(2018)

data <- dt_data_prep(insurance::schedule_p, dt_group_codes)

lobs <- c("workers_compensation", "commercial_auto",
          "private_passenger_auto", "other_liability")

predictions <- lobs %>%
  map(
    function(x) {
      # reinstantiate model
      model <- dt_model()
      
      model %>%
        keras::compile(
          optimizer = keras::optimizer_adam(amsgrad = TRUE),
          loss = "mae",
          loss_weights = c(0.8, 0.2)
      )
      
      c(training_data, validation_data, full_training_data) %<-%
        dt_train_validation_split(data[[x]])
      
      message("Training - ", x)
      
      # determine number of epochs
      epochs_to_train <- dt_optimize_epochs(
        model, training_data, validation_data
      )
      
      model <- dt_model()
      
      model %>% keras::compile(
        optimizer = keras::optimizer_adam(amsgrad = TRUE),
        loss = "mae",
        loss_weights = c(0.8, 0.2)
      )
      
      # fit model to all training data
      history <- model %>%
        fit(x = full_training_data$x,
            y = full_training_data$y,
            batch_size = 128,
            epochs = epochs_to_train,
            verbose = 0)
      dt_compute_predictions(model, data[[x]])
    }) %>%
  bind_rows()

We can then compute performance metrics…

model_results <- dt_compute_metrics(predictions) %>%
  bind_rows(stochastic_model_results) %>%
  bind_rows(read_csv("analysis/automl_results.csv")) %>%
  gather(metric, value, mape, rmspe)

and tabulate the results:

dt_tabulate_metrics(model_results, metric = "mape") %>%
  knitr::kable(booktabs = "T", digits = 3)

lob	Mack	ODP	CIT	LIT	AutoML	DeepTriangle
commercial_auto	0.060	0.217	0.052	0.052	0.068	0.050
other_liability	0.134	0.223	0.165	0.152	0.142	0.120
private_passenger_auto	0.038	0.039	0.038	0.040	0.036	0.023
workers_compensation	0.053	0.105	0.054	0.054	0.067	0.046

dt_tabulate_metrics(model_results, metric = "rmspe") %>%
  knitr::kable(booktabs = "T", digits = 3)

lob	Mack	ODP	CIT	LIT	AutoML	DeepTriangle
commercial_auto	0.080	0.822	0.076	0.074	0.096	0.080
other_liability	0.202	0.477	0.220	0.209	0.181	0.167
private_passenger_auto	0.061	0.063	0.057	0.060	0.059	0.035
workers_compensation	0.079	0.368	0.080	0.080	0.099	0.078

To create actual vs. predicted plots, use the dt_plot_predictions() function.

# devtools::install_github("thomasp85/patchwork")
library(patchwork)
paid_plot <- dt_plot_predictions(predictions, "337", "workers_compensation",
                                 "paid_loss")
case_plot <- dt_plot_predictions(predictions, "337", "workers_compensation",
                                 "claims_outstanding")
paid_plot + case_plot + plot_layout(ncol = 1)

Testing different architectures

If you would like to try out different architectures or hyperparameters, you can do so by providing a function that returns a compiled keras model. See the source code of dt_model() for a template. In order to utilize other functions in this package, the inputs and outputs of your custom function have to match those of dt_model(). You can also implement different early stopping criteria by providing a function similar to dt_optimize_epochs().

For more details on the keras R package, visit https://keras.rstudio.com/.