Getting started with actxps

Simulated data set

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)

census_dat
#> # A tibble: 20,000 × 11
#>    pol_num status   issue_date inc_g…¹ qual    age product gender wd_age pol_val
#>      <int> <fct>    <date>     <lgl>   <lgl> <int> <fct>   <fct>   <int>   <dbl>
#>  1       1 Active   2014-12-17 TRUE    FALSE    56 b       F          77     370
#>  2       2 Surrend… 2007-09-24 FALSE   FALSE    71 a       F          71     708
#>  3       3 Active   2012-10-06 FALSE   TRUE     62 b       F          63     466
#>  4       4 Surrend… 2005-06-27 TRUE    TRUE     62 c       M          62     485
#>  5       5 Active   2019-11-22 FALSE   FALSE    62 c       F          67     978
#>  6       6 Active   2018-09-01 FALSE   TRUE     77 a       F          77    1288
#>  7       7 Active   2011-07-23 TRUE    TRUE     63 a       M          65    1046
#>  8       8 Active   2005-11-08 TRUE    TRUE     58 a       M          58    1956
#>  9       9 Active   2010-09-19 FALSE   FALSE    53 c       M          64    2165
#> 10      10 Active   2012-05-25 TRUE    FALSE    61 b       M          73     609
#> # … with 19,990 more rows, 1 more variable: term_date <date>, and abbreviated
#> #   variable name ¹​inc_guar

The data includes 3 policy statuses: Active, Death, and Surrender.

(status_counts <- table(census_dat$status))
#> 
#>    Active     Death Surrender 
#>     15212      1816      2972

Let’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.

# incorrect
prop.table(status_counts)
#> 
#>    Active     Death Surrender 
#>    0.7606    0.0908    0.1486

Creating exposed data

In 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: 141,252 × 15
#>    pol_num status issue_date inc_guar qual    age product gender wd_age pol_val
#>  *   <int> <fct>  <date>     <lgl>    <lgl> <int> <fct>   <fct>   <int>   <dbl>
#>  1       1 Active 2014-12-17 TRUE     FALSE    56 b       F          77     370
#>  2       1 Active 2014-12-17 TRUE     FALSE    56 b       F          77     370
#>  3       1 Active 2014-12-17 TRUE     FALSE    56 b       F          77     370
#>  4       1 Active 2014-12-17 TRUE     FALSE    56 b       F          77     370
#>  5       1 Active 2014-12-17 TRUE     FALSE    56 b       F          77     370
#>  6       1 Active 2014-12-17 TRUE     FALSE    56 b       F          77     370
#>  7       2 Active 2007-09-24 FALSE    FALSE    71 a       F          71     708
#>  8       2 Active 2007-09-24 FALSE    FALSE    71 a       F          71     708
#>  9       2 Active 2007-09-24 FALSE    FALSE    71 a       F          71     708
#> 10       2 Active 2007-09-24 FALSE    FALSE    71 a       F          71     708
#> # … with 141,242 more rows, and 5 more variables: term_date <date>,
#> #   pol_yr <int>, pol_date_yr <date>, pol_date_yr_end <date>, exposure <dbl>

These functions create exposed_df objects, which are a type of data frame with some additional attributes related to the experience study.

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] 0.02163096

As a default, the expose() function calculates exposures by policy year. This can also be accomplished with the function expose_py(). Other implementations of expose() include:

See vignette("exposures") for further details on exposure calculations.

Experience study summary function

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 × 4
#>   n_claims claims exposure  q_obs
#> *    <int>  <int>    <dbl>  <dbl>
#> 1     2869   2869  132634. 0.0216

See vignette("exp_summary") for further details on exposure calculations.

Grouped experience data

If the data frame passed into exp_stats() is grouped using dplyr::group_by(), 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 × 6
#>    pol_yr inc_guar n_claims claims exposure   q_obs
#>  *  <int> <lgl>       <int>  <int>    <dbl>   <dbl>
#>  1      1 FALSE          56     56    7720. 0.00725
#>  2      1 TRUE           46     46   11532. 0.00399
#>  3      2 FALSE          92     92    7103. 0.0130 
#>  4      2 TRUE           68     68   10612. 0.00641
#>  5      3 FALSE          67     67    6447. 0.0104 
#>  6      3 TRUE           57     57    9650. 0.00591
#>  7      4 FALSE         123    123    5799. 0.0212 
#>  8      4 TRUE           45     45    8737. 0.00515
#>  9      5 FALSE          97     97    5106. 0.0190 
#> 10      5 TRUE           67     67    7810. 0.00858
#> # … with 20 more rows

Actual-to-expected rates

To 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))

# using 2 different expected termination rates
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 × 10
#>    pol_yr inc_g…¹ n_cla…² claims expos…³   q_obs expec…⁴ expec…⁵ ae_ex…⁶ ae_ex…⁷
#>  *  <int> <lgl>     <int>  <int>   <dbl>   <dbl>   <dbl>   <dbl>   <dbl>   <dbl>
#>  1      1 FALSE        56     56   7720. 0.00725 0.005     0.03    1.45    0.242
#>  2      1 TRUE         46     46  11532. 0.00399 0.005     0.015   0.798   0.266
#>  3      2 FALSE        92     92   7103. 0.0130  0.00778   0.03    1.67    0.432
#>  4      2 TRUE         68     68  10612. 0.00641 0.00778   0.015   0.824   0.427
#>  5      3 FALSE        67     67   6447. 0.0104  0.0106    0.03    0.985   0.346
#>  6      3 TRUE         57     57   9650. 0.00591 0.0106    0.015   0.560   0.394
#>  7      4 FALSE       123    123   5799. 0.0212  0.0133    0.03    1.59    0.707
#>  8      4 TRUE         45     45   8737. 0.00515 0.0133    0.015   0.386   0.343
#>  9      5 FALSE        97     97   5106. 0.0190  0.0161    0.03    1.18    0.633
#> 10      5 TRUE         67     67   7810. 0.00858 0.0161    0.015   0.532   0.572
#> # … with 20 more rows, and abbreviated variable names ¹​inc_guar, ²​n_claims,
#> #   ³​exposure, ⁴​expected_1, ⁵​expected_2, ⁶​ae_expected_1, ⁷​ae_expected_2

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 × 8
#>   n_claims claims exposure  q_obs expected_1 expected_2 ae_expected_1 ae_expec…¹
#> *    <int>  <int>    <dbl>  <dbl>      <dbl>      <dbl>         <dbl>      <dbl>
#> 1     2869   2869  132634. 0.0216     0.0242     0.0209         0.892       1.04
#> # … with abbreviated variable name ¹​ae_expected_2

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 × 9
#>   inc_guar n_claims claims exposure  q_obs expected_1 expected_2 ae_ex…¹ ae_ex…²
#> * <lgl>       <int>  <int>    <dbl>  <dbl>      <dbl>      <dbl>   <dbl>   <dbl>
#> 1 FALSE        1601   1601   52123. 0.0307     0.0235      0.03    1.31     1.02
#> 2 TRUE         1268   1268   80511. 0.0157     0.0247      0.015   0.637    1.05
#> # … with abbreviated variable names ¹​ae_expected_1, ²​ae_expected_2

Shiny App

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)