Experience studies are used by actuaries to explore historical experience across blocks of business and to inform assumption setting activities. This package provides functions for preparing data, creating studies, and beginning assumption development.
You can install the development version of actxps from
GitHub with:
# install.packages("devtools")
devtools::install_github("mattheaphy/actxps")The actxps package includes a data frame containing
simulated census data for a theoretical deferred annuity product with an
optional guaranteed income rider. The grain of this data is one row per
policy.
library(actxps)
library(dplyr)
#>
#> Attaching package: 'dplyr'
#> The following objects are masked from 'package:stats':
#>
#> filter, lag
#> The following objects are masked from 'package:base':
#>
#> intersect, setdiff, setequal, union
census_dat
#> # A tibble: 20,000 x 10
#> pol_num status issue_date inc_guar qual age product gender wd_age
#> <int> <fct> <date> <lgl> <lgl> <int> <fct> <fct> <int>
#> 1 1 Active 2014-12-17 TRUE FALSE 56 b F 77
#> 2 2 Surrender 2007-09-24 FALSE FALSE 71 a F 71
#> 3 3 Active 2012-10-06 FALSE TRUE 62 b F 63
#> 4 4 Surrender 2005-06-27 TRUE TRUE 62 c M 62
#> 5 5 Active 2019-11-22 FALSE FALSE 62 c F 67
#> 6 6 Active 2018-09-01 FALSE TRUE 77 a F 77
#> 7 7 Active 2011-07-23 TRUE TRUE 63 a M 65
#> 8 8 Surrender 2005-11-08 TRUE TRUE 58 a M 58
#> 9 9 Active 2010-09-19 FALSE FALSE 53 c M 64
#> 10 10 Active 2012-05-25 TRUE FALSE 61 b M 73
#> # ... with 19,990 more rows, and 1 more variable: term_date <date>The data includes 3 policy statuses: Active, Death, and Surrender.
(status_counts <- table(census_dat$status))
#>
#> Active Death Surrender
#> 15195 1860 2945Let’s assume we’re interested in calculating the probability of surrender over one policy year. We cannot simply calculate the proportion of policies in a surrendered status as this does not represent an annualized surrender rate.
prop.table(status_counts)
#>
#> Active Death Surrender
#> 0.75975 0.09300 0.14725In order to calculate annual surrender rates, we need to break each policy into multiple records. There should be one row per policy per year.
The expose_ family of functions is used to perform this
transformation.
exposed_data <- expose(census_dat, end_date = "2019-12-31",
target_status = "Surrender")
exposed_data
#> Exposure data
#>
#> Exposure type: policy_year
#> Target status: Surrender
#> Study range: 1900-01-01 to 2019-12-31
#>
#> # A tibble: 141,297 x 13
#> pol_num status issue_date inc_guar qual age product gender wd_age
#> * <int> <fct> <date> <lgl> <lgl> <int> <fct> <fct> <int>
#> 1 1 Active 2014-12-17 TRUE FALSE 56 b F 77
#> 2 1 Active 2014-12-17 TRUE FALSE 56 b F 77
#> 3 1 Active 2014-12-17 TRUE FALSE 56 b F 77
#> 4 1 Active 2014-12-17 TRUE FALSE 56 b F 77
#> 5 1 Active 2014-12-17 TRUE FALSE 56 b F 77
#> 6 1 Active 2014-12-17 TRUE FALSE 56 b F 77
#> 7 2 Active 2007-09-24 FALSE FALSE 71 a F 71
#> 8 2 Active 2007-09-24 FALSE FALSE 71 a F 71
#> 9 2 Active 2007-09-24 FALSE FALSE 71 a F 71
#> 10 2 Active 2007-09-24 FALSE FALSE 71 a F 71
#> # ... with 141,287 more rows, and 4 more variables: term_date <date>,
#> # pol_yr <int>, pol_date_yr <date>, exposure <dbl>Now that the data has been “exposed” by policy year, the observed annual surrender probability can be calculated as:
sum(exposed_data$status == "Surrender") / sum(exposed_data$exposure)
#> [1] 0.02145196As a default, the expose function calculate exposures by
policy year. This can also be accomplished with the function
expose_py. Other implementations of expose
include:
expose_cy = exposures by calendar yearexpose_cq = exposures by calendar quarterexpose_pm = exposures by policy monthexpose_cm = exposures by calendar monthAll expose_ functions return exposed_df
objects.
The exp_stats function creates a summary of observed
experience data. The output of this function is an exp_df
object.
exp_stats(exposed_data)
#> Experience study results
#>
#> Groups:
#> Target status: Surrender
#> Study range: 1900-01-01 to 2019-12-31
#>
#> # A tibble: 1 x 4
#> n_claims claims exposure q_obs
#> * <int> <int> <dbl> <dbl>
#> 1 2846 2846 132669. 0.0215If the data frame passed into exp_stats is grouped, the
resulting output will contain one record for each unique group.
library(dplyr)
exp_res <- exposed_data |>
group_by(pol_yr, inc_guar) |>
exp_stats()
exp_res
#> Experience study results
#>
#> Groups: pol_yr, inc_guar
#> Target status: Surrender
#> Study range: 1900-01-01 to 2019-12-31
#>
#> # A tibble: 30 x 6
#> pol_yr inc_guar n_claims claims exposure q_obs
#> * <int> <lgl> <int> <int> <dbl> <dbl>
#> 1 1 FALSE 42 42 7719. 0.00544
#> 2 1 TRUE 38 38 11526. 0.00330
#> 3 2 FALSE 65 65 7117. 0.00913
#> 4 2 TRUE 61 61 10605. 0.00575
#> 5 3 FALSE 67 67 6476. 0.0103
#> 6 3 TRUE 60 60 9626. 0.00623
#> 7 4 FALSE 103 103 5823. 0.0177
#> 8 4 TRUE 58 58 8697. 0.00667
#> 9 5 FALSE 94 94 5147. 0.0183
#> 10 5 TRUE 72 72 7779. 0.00926
#> # ... with 20 more rowsTo derive actual-to-expected rates, first attach one or more columns
of expected termination rates to the exposure data. Then, pass these
column names to the expected argument of
exp_stats.
expected_table <- c(seq(0.005, 0.03, length.out = 10), 0.2, 0.15, rep(0.05, 3))
exposed_data <- exposed_data |>
mutate(expected_1 = expected_table[pol_yr],
expected_2 = ifelse(exposed_data$inc_guar, 0.015, 0.03))
exp_res <- exposed_data |>
group_by(pol_yr, inc_guar) |>
exp_stats(expected = c("expected_1", "expected_2"))
exp_res
#> Experience study results
#>
#> Groups: pol_yr, inc_guar
#> Target status: Surrender
#> Study range: 1900-01-01 to 2019-12-31
#> Expected values: expected_1, expected_2
#>
#> # A tibble: 30 x 10
#> pol_yr inc_guar n_claims claims exposure q_obs expected_1 expected_2
#> * <int> <lgl> <int> <int> <dbl> <dbl> <dbl> <dbl>
#> 1 1 FALSE 42 42 7719. 0.00544 0.005 0.03
#> 2 1 TRUE 38 38 11526. 0.00330 0.005 0.015
#> 3 2 FALSE 65 65 7117. 0.00913 0.00778 0.03
#> 4 2 TRUE 61 61 10605. 0.00575 0.00778 0.015
#> 5 3 FALSE 67 67 6476. 0.0103 0.0106 0.03
#> 6 3 TRUE 60 60 9626. 0.00623 0.0106 0.015
#> 7 4 FALSE 103 103 5823. 0.0177 0.0133 0.03
#> 8 4 TRUE 58 58 8697. 0.00667 0.0133 0.015
#> 9 5 FALSE 94 94 5147. 0.0183 0.0161 0.03
#> 10 5 TRUE 72 72 7779. 0.00926 0.0161 0.015
#> # ... with 20 more rows, and 2 more variables: ae_expected_1 <dbl>,
#> # ae_expected_2 <dbl>autoplot() and
autotable()The autoplot() and autotable() functions
can be used to create visualizations and summary tables.
library(ggplot2)
.colors <- c("#eb15e4", "#7515eb")
theme_set(theme_light())
exp_res |>
autoplot() +
scale_color_manual(values = .colors) +
labs(title = "Observed Surrender Rates by Policy Year and Income Guarantee Presence")
autotable(exp_res)
summary()Calling the summary function on an exp_df
object re-summarizes experience results. This also produces an
exp_df object.
summary(exp_res)
#> Experience study results
#>
#> Groups:
#> Target status: Surrender
#> Study range: 1900-01-01 to 2019-12-31
#> Expected values: expected_1, expected_2
#>
#> # A tibble: 1 x 8
#> n_claims claims exposure q_obs expected_1 expected_2 ae_expected_1
#> * <int> <int> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 2846 2846 132669. 0.0215 0.0242 0.0209 0.885
#> # ... with 1 more variable: ae_expected_2 <dbl>If additional variables are passed to ..., these
variables become groups in the re-summarized exp_df
object.
summary(exp_res, inc_guar)
#> Experience study results
#>
#> Groups: inc_guar
#> Target status: Surrender
#> Study range: 1900-01-01 to 2019-12-31
#> Expected values: expected_1, expected_2
#>
#> # A tibble: 2 x 9
#> inc_guar n_claims claims exposure q_obs expected_1 expected_2 ae_expected_1
#> * <lgl> <int> <int> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 FALSE 1615 1615 52338. 0.0309 0.0234 0.03 1.32
#> 2 TRUE 1231 1231 80331. 0.0153 0.0248 0.015 0.619
#> # ... with 1 more variable: ae_expected_2 <dbl>Passing an exposed_df object to the
exp_shiny function launches a shiny app that enables
interactive exploration of experience data.
exp_shiny(exposed_data)