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Reserve risk is material...

...but it's hard to estimate!

...but it's hard to estimate!

And some don't appreciate that...

But are they accurate? We can test that!

Meyers's Monograph

Back-testing methodology

Back-testing methodology

Monograph summary and conclusion

So build an R package!

Example: "training data"

cas_loss_reserve_db %>%
  get_meyers_subset() %>%
  filter(line == "ppauto" & group_id == 388) %>%
  pluck("train_tri_set", 1, "paid")

##       dev_lag
## acc_yr     1     2     3     4     5     6     7     8     9    10
##   1988 13440 35680 48703 56319 61018 61119 63049 63556 63744 63835
##   1989 18757 44166 57578 66264 65600 67721 75369 76713 77007    NA
##   1990 19834 42225 56347 63194 67112 69459 74267 79208    NA    NA
##   1991 16230 38045 46055 53983 60638 62917 71074    NA    NA    NA
##   1992 14629 22427 33873 43339 53168 60413    NA    NA    NA    NA
##   1993 24597 51373 68484 80253 92192    NA    NA    NA    NA    NA
##   1994 31723 59733 77398 94395    NA    NA    NA    NA    NA    NA
##   1995 37397 71133 94294    NA    NA    NA    NA    NA    NA    NA
##   1996 53670 98628    NA    NA    NA    NA    NA    NA    NA    NA
##   1997 52837    NA    NA    NA    NA    NA    NA    NA    NA    NA
## attr(,"class")
## [1] "triangle" "matrix"  
## attr(,"exposure")
##  [1]  83473  91800  95877  99256  96170 139038 152174 167833 180523 164717

Example: "testing data"

cas_loss_reserve_db %>%
  get_meyers_subset() %>%
  filter(line == "ppauto" & group_id == 388) %>%
  pluck("test_tri_set", 1, "paid")

##       dev_lag
## acc_yr     2      3      4      5      6      7      8      9     10
##   1988    NA     NA     NA     NA     NA     NA     NA     NA  63835
##   1989    NA     NA     NA     NA     NA     NA     NA     NA  77029
##   1990    NA     NA     NA     NA     NA     NA     NA  79250  79308
##   1991    NA     NA     NA     NA     NA     NA  71885  72560  72579
##   1992    NA     NA     NA     NA     NA  61452  62363  62464  62458
##   1993    NA     NA     NA     NA  94939  97226  97536  97654  97787
##   1994    NA     NA     NA 101008 104557 107399 108067 108476 110038
##   1995    NA     NA 103996 107948 109478 110401 111051 111108 111598
##   1996    NA 112473 123070 129739 131549 132682 133137 133426 133522
##   1997 77758  95357 104789 109025 111835 112467 113000 113086 113371
## attr(,"class")
## [1] "triangle" "matrix"

Example: Commercial Auto

Now we can run the Mack method on our triangle training data and back-test its accuracy. We use the implementation of the Mack method in the ChainLadder package, MackChainLadder, applied to the comauto line of business.

cas_db_subset <- cas_loss_reserve_db %>%
  get_meyers_subset()
mack_paid_results <- run_single_backtest(cas_db_subset, 
                                         testr_MackChainLadder, 
                                         lines_to_include = "comauto",
                                         loss_type_to_backtest = "paid", 
                                         method_label = "mack_paid")

Example: Commercial Auto - output

glimpse(mack_paid_results)

## Observations: 47
## Variables: 11
## $ line              <chr> "comauto", "comauto", "comauto", "comauto", ...
## $ group_id          <dbl> 353, 388, 620, 833, 1066, 1090, 1538, 1767, ...
## $ company           <chr> "Celina Mut Grp", "Federal Ins Co Grp", "Emp...
## $ method            <chr> "mack_paid", "mack_paid", "mack_paid", "mack...
## $ actual_ultimate   <dbl> 40000, 745997, 388485, 24613, 63022, 21354, ...
## $ actual_unpaid     <dbl> 7399, 189270, 89855, 2959, 5269, 3474, 16640...
## $ mean_ultimate_est <dbl> 39177.438, 714600.238, 398408.978, 25350.326...
## $ mean_unpaid_est   <dbl> 6576.4378, 157873.2378, 99778.9781, 3696.325...
## $ stddev_est        <dbl> 1442.5094, 46454.1901, 9466.1578, 836.7769, ...
## $ cv_unpaid_est     <dbl> 0.21934510, 0.29424994, 0.09487126, 0.226380...
## $ implied_pctl      <dbl> 0.7200268344, 0.7563488511, 0.1468789988, 0....

Example: Commercial Auto - results

create_pp_plot(mack_paid_results, by_line = TRUE)

Mack - Paid

create_pp_plot(mack_paid_results_all, by_line = TRUE)

Mack - Case-Incurred

create_pp_plot(mack_case_results_all, by_line = TRUE)

ODP Bootstrap - Paid

create_pp_plot(boot_paid_results_all, by_line = TRUE)

ODP Bootstrap - Case-Incurred

create_pp_plot(boot_case_results_all, by_line = TRUE)

Clark Cape Cod - Paid

create_pp_plot(clark_paid_results_all, by_line = TRUE)

Clark Cape Cod - Case-Incurred

create_pp_plot(clark_case_results_all, by_line = TRUE)

Changing Settlement Rate - Paid

reservetestr enhancements

Contact

• adam.troyer@aonbenfield.com