actxps

The actxps package provides a set of tools to assist with the creation of actuarial experience studies. Experience studies are used by actuaries to explore historical experience across blocks of business and to inform assumption setting for projection models.

• The ExposedDF class converts census-level records into policy or calendar year exposure records.
• The exp_stats() method of ExposedDF creates ExpStats experience summary objects containing observed termination rates and claims. Optionally, expected termination rates, actual-to-expected ratios, and limited fluctuation credibility estimates can also be returned.
• The add_transactions() method of ExposedDF attaches summarized transactions to an ExposedDF object.
• The trx_stats() method of ExposedDF creates TrxStats transaction summary objects containing transaction counts, amounts, frequencies, and utilization. Optionally, transaction amounts can be expressed as a percentage of one or more variables to calculate rates or actual-to-expected ratios.
• The plot() and table() methods of ExpStats and TrxStats create plots and tables for reporting.
• The exp_shiny() method of ExposedDF launches a Shiny app that allows for interactive exploration of experience drivers.

Installation

The actxps package can be installed from PyPI with:

$ pip install actxps

Basic usage

An expanded version of this demo is available at Getting started with actxps.

The actxps package includes 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.

import actxps as xp
import numpy as np
import polars as pl

census_dat = xp.load_census_dat()
print(census_dat)

shape: (20_000, 11)
┌─────────┬───────────┬────────────┬──────────┬───┬────────┬────────┬─────────┬────────────┐
│ pol_num ┆ status    ┆ issue_date ┆ inc_guar ┆ … ┆ gender ┆ wd_age ┆ premium ┆ term_date  │
│ ---     ┆ ---       ┆ ---        ┆ ---      ┆   ┆ ---    ┆ ---    ┆ ---     ┆ ---        │
│ i64     ┆ cat       ┆ date       ┆ bool     ┆   ┆ cat    ┆ i64    ┆ f64     ┆ date       │
╞═════════╪═══════════╪════════════╪══════════╪═══╪════════╪════════╪═════════╪════════════╡
│ 1       ┆ Active    ┆ 2014-12-17 ┆ true     ┆ … ┆ F      ┆ 77     ┆ 370.0   ┆ null       │
│ 2       ┆ Surrender ┆ 2007-09-24 ┆ false    ┆ … ┆ F      ┆ 71     ┆ 708.0   ┆ 2019-03-08 │
│ 3       ┆ Active    ┆ 2012-10-06 ┆ false    ┆ … ┆ F      ┆ 63     ┆ 466.0   ┆ null       │
│ 4       ┆ Surrender ┆ 2005-06-27 ┆ true     ┆ … ┆ M      ┆ 62     ┆ 485.0   ┆ 2018-11-29 │
│ 5       ┆ Active    ┆ 2019-11-22 ┆ false    ┆ … ┆ F      ┆ 67     ┆ 978.0   ┆ null       │
│ …       ┆ …         ┆ …          ┆ …        ┆ … ┆ …      ┆ …      ┆ …       ┆ …          │
│ 19996   ┆ Active    ┆ 2014-08-11 ┆ true     ┆ … ┆ F      ┆ 75     ┆ 3551.0  ┆ null       │
│ 19997   ┆ Surrender ┆ 2006-11-20 ┆ false    ┆ … ┆ F      ┆ 77     ┆ 336.0   ┆ 2017-07-09 │
│ 19998   ┆ Surrender ┆ 2017-02-20 ┆ true     ┆ … ┆ F      ┆ 68     ┆ 1222.0  ┆ 2018-08-03 │
│ 19999   ┆ Active    ┆ 2015-04-11 ┆ false    ┆ … ┆ M      ┆ 78     ┆ 2138.0  ┆ null       │
│ 20000   ┆ Active    ┆ 2009-04-29 ┆ true     ┆ … ┆ M      ┆ 72     ┆ 5751.0  ┆ null       │
└─────────┴───────────┴────────────┴──────────┴───┴────────┴────────┴─────────┴────────────┘

Convert census records to exposure records with one row per policy per year.

exposed_data = xp.ExposedDF(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

shape: (141_252, 15)
┌─────────┬────────┬────────────┬──────────┬───┬────────┬─────────────┬─────────────────┬──────────┐
│ pol_num ┆ status ┆ issue_date ┆ inc_guar ┆ … ┆ pol_yr ┆ pol_date_yr ┆ pol_date_yr_end ┆ exposure │
│ ---     ┆ ---    ┆ ---        ┆ ---      ┆   ┆ ---    ┆ ---         ┆ ---             ┆ ---      │
│ i64     ┆ enum   ┆ date       ┆ bool     ┆   ┆ u32    ┆ date        ┆ date            ┆ f64      │
╞═════════╪════════╪════════════╪══════════╪═══╪════════╪═════════════╪═════════════════╪══════════╡
│ 1       ┆ Active ┆ 2014-12-17 ┆ true     ┆ … ┆ 1      ┆ 2014-12-17  ┆ 2015-12-16      ┆ 1.0      │
│ 1       ┆ Active ┆ 2014-12-17 ┆ true     ┆ … ┆ 2      ┆ 2015-12-17  ┆ 2016-12-16      ┆ 1.0      │
│ 1       ┆ Active ┆ 2014-12-17 ┆ true     ┆ … ┆ 3      ┆ 2016-12-17  ┆ 2017-12-16      ┆ 1.0      │
│ 1       ┆ Active ┆ 2014-12-17 ┆ true     ┆ … ┆ 4      ┆ 2017-12-17  ┆ 2018-12-16      ┆ 1.0      │
│ 1       ┆ Active ┆ 2014-12-17 ┆ true     ┆ … ┆ 5      ┆ 2018-12-17  ┆ 2019-12-16      ┆ 1.0      │
│ …       ┆ …      ┆ …          ┆ …        ┆ … ┆ …      ┆ …           ┆ …               ┆ …        │
│ 20000   ┆ Active ┆ 2009-04-29 ┆ true     ┆ … ┆ 7      ┆ 2015-04-29  ┆ 2016-04-28      ┆ 1.0      │
│ 20000   ┆ Active ┆ 2009-04-29 ┆ true     ┆ … ┆ 8      ┆ 2016-04-29  ┆ 2017-04-28      ┆ 1.0      │
│ 20000   ┆ Active ┆ 2009-04-29 ┆ true     ┆ … ┆ 9      ┆ 2017-04-29  ┆ 2018-04-28      ┆ 1.0      │
│ 20000   ┆ Active ┆ 2009-04-29 ┆ true     ┆ … ┆ 10     ┆ 2018-04-29  ┆ 2019-04-28      ┆ 1.0      │
│ 20000   ┆ Active ┆ 2009-04-29 ┆ true     ┆ … ┆ 11     ┆ 2019-04-29  ┆ 2020-04-28      ┆ 0.674863 │
└─────────┴────────┴────────────┴──────────┴───┴────────┴─────────────┴─────────────────┴──────────┘

Create a summary grouped by policy year and the presence of a guaranteed income rider.

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

shape: (30, 6)
┌────────┬──────────┬──────────┬────────┬──────────────┬──────────┐
│ pol_yr ┆ inc_guar ┆ n_claims ┆ claims ┆ exposure     ┆ q_obs    │
│ ---    ┆ ---      ┆ ---      ┆ ---    ┆ ---          ┆ ---      │
│ u32    ┆ bool     ┆ u32      ┆ u32    ┆ f64          ┆ f64      │
╞════════╪══════════╪══════════╪════════╪══════════════╪══════════╡
│ 1      ┆ false    ┆ 56       ┆ 56     ┆ 7719.80774   ┆ 0.007254 │
│ 1      ┆ true     ┆ 46       ┆ 46     ┆ 11532.404626 ┆ 0.003989 │
│ 2      ┆ false    ┆ 92       ┆ 92     ┆ 7102.81316   ┆ 0.012953 │
│ 2      ┆ true     ┆ 68       ┆ 68     ┆ 10611.967258 ┆ 0.006408 │
│ 3      ┆ false    ┆ 67       ┆ 67     ┆ 6446.916146  ┆ 0.010393 │
│ …      ┆ …        ┆ …        ┆ …      ┆ …            ┆ …        │
│ 13     ┆ true     ┆ 49       ┆ 49     ┆ 1117.137361  ┆ 0.043862 │
│ 14     ┆ false    ┆ 33       ┆ 33     ┆ 262.622262   ┆ 0.125656 │
│ 14     ┆ true     ┆ 29       ┆ 29     ┆ 609.216476   ┆ 0.047602 │
│ 15     ┆ false    ┆ 8        ┆ 8      ┆ 74.050109    ┆ 0.108035 │
│ 15     ┆ true     ┆ 9        ┆ 9      ┆ 194.128602   ┆ 0.046361 │
└────────┴──────────┴──────────┴────────┴──────────────┴──────────┘

Calculate actual-to-expected ratios.

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 = np.concatenate((
    np.linspace(0.005, 0.03, 10), 
    np.array([0.2, 0.15]), 
    np.repeat(0.05, 3)
    ))

# using 2 different expected termination rates
exposed_data.data = exposed_data.data.with_columns(
    expected_1=expected_table[exposed_data.data['pol_yr'] - 1],
    expected_2=pl.when(pl.col('inc_guar')).then(0.015).otherwise(0.03)
)

exp_res = (exposed_data.
           group_by('pol_yr', 'inc_guar').
           exp_stats(expected = ["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

shape: (30, 10)
┌────────┬──────────┬──────────┬────────┬───┬────────────┬────────────┬──────────────┬─────────────┐
│ pol_yr ┆ inc_guar ┆ n_claims ┆ claims ┆ … ┆ expected_1 ┆ expected_2 ┆ ae_expected_ ┆ ae_expected │
│ ---    ┆ ---      ┆ ---      ┆ ---    ┆   ┆ ---        ┆ ---        ┆ 1            ┆ _2          │
│ u32    ┆ bool     ┆ u32      ┆ u32    ┆   ┆ f64        ┆ f64        ┆ ---          ┆ ---         │
│        ┆          ┆          ┆        ┆   ┆            ┆            ┆ f64          ┆ f64         │
╞════════╪══════════╪══════════╪════════╪═══╪════════════╪════════════╪══════════════╪═════════════╡
│ 1      ┆ false    ┆ 56       ┆ 56     ┆ … ┆ 0.005      ┆ 0.03       ┆ 1.450813     ┆ 0.241802    │
│ 1      ┆ true     ┆ 46       ┆ 46     ┆ … ┆ 0.005      ┆ 0.015      ┆ 0.797752     ┆ 0.265917    │
│ 2      ┆ false    ┆ 92       ┆ 92     ┆ … ┆ 0.007778   ┆ 0.03       ┆ 1.665336     ┆ 0.431754    │
│ 2      ┆ true     ┆ 68       ┆ 68     ┆ … ┆ 0.007778   ┆ 0.015      ┆ 0.823868     ┆ 0.427191    │
│ 3      ┆ false    ┆ 67       ┆ 67     ┆ … ┆ 0.010556   ┆ 0.03       ┆ 0.984559     ┆ 0.346419    │
│ …      ┆ …        ┆ …        ┆ …      ┆ … ┆ …          ┆ …          ┆ …            ┆ …           │
│ 13     ┆ true     ┆ 49       ┆ 49     ┆ … ┆ 0.05       ┆ 0.015      ┆ 0.877242     ┆ 2.924141    │
│ 14     ┆ false    ┆ 33       ┆ 33     ┆ … ┆ 0.05       ┆ 0.03       ┆ 2.513115     ┆ 4.188525    │
│ 14     ┆ true     ┆ 29       ┆ 29     ┆ … ┆ 0.05       ┆ 0.015      ┆ 0.952043     ┆ 3.173475    │
│ 15     ┆ false    ┆ 8        ┆ 8      ┆ … ┆ 0.05       ┆ 0.03       ┆ 2.160699     ┆ 3.601165    │
│ 15     ┆ true     ┆ 9        ┆ 9      ┆ … ┆ 0.05       ┆ 0.015      ┆ 0.92722      ┆ 3.090735    │
└────────┴──────────┴──────────┴────────┴───┴────────────┴────────────┴──────────────┴─────────────┘

Create visualizations using the plot() and table() methods.

exp_res.plot()

<Figure Size: (640 x 480)>

# first 10 rows showed for brevity
exp_res.table()

Launch a shiny app to interactively explore experience data.

exposed_data.exp_shiny()

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