Individual claims reserving using the Aalen-Johansen estimator

This repository contains the code to replicate the manuscript Individual claims reserving using the Aalen-Johansen estimator.

The replication material is organized as described in this file and it can be used for replicating exactly the results of our manuscript.

The script elaborate_latex_tables.R contains the code to print the tables in the manuscript from the the results in the results_csv folder.

The script helper_functions_ajr.R contains functions that we used to perform the calculations.

The real data that we used in our application will not be shared, but we provide the results that we obtained.

For each section, we describe below the relevant replication material.

Section 4. Simulation of RBNS claims

Section 4.1. Implementation

• Figure 2 can be reproduced with the script figure_2.R.

Section 4.2. Evaluating the models performance

• Figure 3 can be reproduced with the script figure_3.R.

Section 4.3. Empirical analysis

• Table 1 can be reproduced with the script table_1.R.

• Table 2 can be reproduced with the scripts table_2_intercept_model.R (results for the intercept model) and table_2_feature_model.R (results for the model with feature).

Section 4.4 Comparison with hirem

• Table 3 can be reproduced with the script table_2_feature_model.R.

• Table 5 can be reproduced with the script table_5_comparison_with_hirem.R.

Section 5. A data application on an insurance portfolio

• We obtained Figure 4 with the script figure_4.R.

• We obtained Figure 5 with the script figure_5.R.

Section 5.1. Model comparison on different datasets

• We obtained Table 6 and Table 7 using the script table_6_intercept_model.R(results for the intercept model) and table_6_feature_model.R (results for the model with feature).

Section 5.2. Model comparison on a single dataset

• We obtained Table 8 using the scripts table_8_intercept_model.R (results for the intercept model) and table_8_feature_model.R (results for the model with feature).

Content of the results_csv folder

• Results of scenario Alpha:

  • simulation_no_features_all_records_4_2023_10_23_11_57.csv
  • simulation_no_features_all_records_5_2023_10_23_11_58.csv
  • simulation_no_features_all_records_6_2023_10_23_12_00.csv
  • simulation_no_features_all_records_7_2023_10_23_15_16.csv

• Results of scenario Beta:

  • Intercept model

    • simulation_aytrend_interceptmodel_all_records_4_2023_10_24_16_27.csv
    • simulation_aytrend_interceptmodel_all_records_5_2023_10_24_17_36.csv
    • simulation_aytrend_interceptmodel_all_records_6_2023_10_24_16_31.csv
    • simulation_aytrend_interceptmodel_all_records_7_2023_10_24_16_32.csv

  • Model with feature

    • simulation_aytrend4_2024_02_29_13_31.csv
    • simulation_aytrend5_2024_02_29_13_32.csv
    • simulation_aytrend6_2024_02_29_13_34.csv
    • simulation_aytrend7_2024_02_29_13_36.csv

• Comparison with hirem (Section 4.4.):

  • simulation_hirem_10.csv
  • simulation_hirem_extreme_10.csv
  • simulation_hirem_settlement_10.csv
  • simulation_hirem_claimmix_10.csv

• Results on the real data (Section 5.1.):

  • real_data_w_features__2023_11_02_10_42.csv
  • real_data_no_features__2023_11_02_09_58.csv

• Results on the real data (Section 5.2.):

  • real_data_w_features_maxp_6_2023_11_02_11_27.csv
  • real_data_no_features_maxp_6_2023_11_02_09_29.csv

Current R Session

Using the command sessionInfo(), we report version information about R, the OS and attached or loaded packages.

R version 4.3.0 (2023-04-21 ucrt)
Platform: x86_64-w64-mingw32/x64 (64-bit)
Running under: Windows 11 x64 (build 22631)

Matrix products: default


locale:
[1] LC_COLLATE=English_United States.utf8  LC_CTYPE=English_United States.utf8    LC_MONETARY=English_United States.utf8
[4] LC_NUMERIC=C                           LC_TIME=English_United States.utf8    

time zone: Europe/Rome
tzcode source: internal

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
[1] hirem_0.1.0        ChainLadder_0.2.18 tidyr_1.3.1        dplyr_1.1.2        ggplot2_3.5.0      xtable_1.8-4      
[7] data.table_1.14.8 

loaded via a namespace (and not attached):
 [1] cplm_0.7-11       gtable_0.3.4      biglm_0.9-2.1     gbm_2.1-06        xfun_0.39         lattice_0.21-8   
 [7] vctrs_0.6.2       tools_4.3.0       generics_0.1.3    stats4_4.3.0      parallel_4.3.0    sandwich_3.0-2   
[13] tibble_3.2.1      fansi_1.0.4       pkgconfig_2.0.3   Matrix_1.6-1.1    actuar_3.3-2      lifecycle_1.0.4  
[19] compiler_4.3.0    stringr_1.5.1     statmod_1.5.0     munsell_0.5.0     systemfit_1.1-30  carData_3.0-5    
[25] htmltools_0.5.5   yaml_2.3.7        pillar_1.9.0      car_3.1-2         MASS_7.3-58.4     abind_1.4-5      
[31] nlme_3.1-162      tidyselect_1.2.0  digest_0.6.31     stringi_1.7.12    reshape2_1.4.4    purrr_1.0.1      
[37] splines_4.3.0     fastmap_1.1.1     grid_4.3.0        colorspace_2.1-0  cli_3.6.1         magrittr_2.0.3   
[43] survival_3.5-5    utf8_1.2.3        withr_3.0.0       scales_1.3.0      bit64_4.0.5       tweedie_2.3.5    
[49] lubridate_1.9.2   timechange_0.2.0  rmarkdown_2.21    bit_4.0.5         AalenJohansen_1.0 zoo_1.8-12       
[55] expint_0.1-8      coda_0.19-4       evaluate_0.21     knitr_1.42        lmtest_0.9-40     rlang_1.1.3      
[61] Rcpp_1.0.10       glue_1.6.2        DBI_1.1.3         rstudioapi_0.15.0 minqa_1.2.5       R6_2.5.1         
[67] plyr_1.8.8