Exposure Calculation with ExperienceAnalysis.jl

Available Exposure Basis

• ExperienceAnalysis.Anniversary(period) will give exposures periods based on the first date
• ExperienceAnalysis.Calendar(period) will follow calendar periods (e.g. month or year)
• ExperienceAnalysis.AnniversaryCalendar(period,period) will split into the smaller of the calendar or policy anniversary period.

Where period is a Period Type from the Dates standard library.

Calculate exposures with exposure(basis, from, to, continued_exposure; study_start, study_end).

• continued_exposure indicates whether the exposure should be extended through the full exposure period rather than terminate at the to date.

Full Example

We’ll start with this as our data:

using DataFrames
df = DataFrame(
    id=[1, 2, 3],
    issue=[Date(2016, 7, 4), Date(2016, 1, 1), Date(2016, 1, 1)],
    end_date=[Date(2020, 1, 17), Date(2018, 5, 4), Date(2020, 12, 31)],
    status=["Claim", "Lapse", "Inforce"]
)

Define the start and end of the study:

study_end = Date(2020, 6, 30)
study_start = Date(2018, 6, 30)

2018-06-30

Calculate the exposure by broadcasting the exposure function over the three arrays we are passing to it:

df.exposure = exposure.(
    ExperienceAnalysis.Anniversary(Year(1)),   # The basis for our exposures
    df.issue,                                  # The `from` date
    df.end_date,                               # the last observed date
    df.status .== "Claim";                        # a boolean vector indicating continuation
    study_start=study_start,
    study_end=study_end
)

3-element Vector{Vector{@NamedTuple{from::Date, to::Date, policy_timestep::Int64}}}:
 [(from = Date("2018-06-30"), to = Date("2018-07-03"), policy_timestep = 2), (from = Date("2018-07-04"), to = Date("2019-07-03"), policy_timestep = 3), (from = Date("2019-07-04"), to = Date("2020-07-03"), policy_timestep = 4)]
 []
 [(from = Date("2018-06-30"), to = Date("2018-12-31"), policy_timestep = 3), (from = Date("2019-01-01"), to = Date("2019-12-31"), policy_timestep = 4), (from = Date("2020-01-01"), to = Date("2020-06-30"), policy_timestep = 5)]

In our dataframe, we actually have a column that contains an array of tuples now, so to expand it so that each exposure period gets a row, we flatten the dataframe to get our exposures:

df = flatten(df, :exposure)

using DayCounts

# note: the `to` date is inclusive, so we add a day when computing the fraction
df.exposure_fraction = map(e -> yearfrac(e.from, e.to + Day(1), DayCounts.Thirty360()), df.exposure)
df[:, [:exposure, :exposure_fraction]]

Discussion and Questions

If you have other ideas or questions, feel free to also open an issue, or discuss on the community Zulip or Slack #actuary channel. We welcome all actuarial and related disciplines!