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@alecloudenback
alecloudenback committed Jun 5, 2024
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200 changes: 182 additions & 18 deletions README.md
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Original file line number Diff line number Diff line change
Expand Up @@ -10,21 +10,17 @@ Calculate exposures.
## Quickstart

```julia
using ExperienceAnalysis
using DataFrames
using Dates

df = DataFrame(
policy_id = 1:3,
issue_date = [Date(2020,5,10), Date(2020,4,5), Date(2019, 3, 10)],
termination_date = [Date(2022, 6, 10), Date(2022, 8, 10), nothing],
end_date = [Date(2022, 6, 10), Date(2022, 8, 10), Date(2022,12,31)],
status = ["claim", "lapse", "inforce"]
)

df.policy_year = exposure.(
ExperienceAnalysis.Anniversary(Year(1)),
df.issue_date,
df.termination_date,
df.end_date,
df.status .== "claim"; # continued exposure
study_start = Date(2020, 1, 1),
study_end = Date(2022, 12, 31)
Expand All @@ -38,18 +34,19 @@ df.exposure_fraction =
# here we end the interval at Date(2020, 12, 31), so we need to add a day to get the correct exposure fraction.
```

policy_id | issue_date | termination_date | status | policy_year | exposure_fraction
--- | --- | --- | --- | --- | ---
1 | 2020-05-10 | 2022-06-10 | claim | (from = Date("2020-05-10"), to = Date("2021-05-09"), policy_timestep = 1) | 1.0
1 | 2020-05-10 | 2022-06-10 | claim | (from = Date("2021-05-10"), to = Date("2022-05-09"), policy_timestep = 2) | 1.0
1 | 2020-05-10 | 2022-06-10 | claim | (from = Date("2022-05-10"), to = Date("2023-05-09"), policy_timestep = 3) | 1.0
2 | 2020-04-05 | 2022-08-10 | lapse | (from = Date("2020-04-05"), to = Date("2021-04-04"), policy_timestep = 1) | 1.0
2 | 2020-04-05 | 2022-08-10 | lapse | (from = Date("2021-04-05"), to = Date("2022-04-04"), policy_timestep = 2) | 1.0
2 | 2020-04-05 | 2022-08-10 | lapse | (from = Date("2022-04-05"), to = Date("2022-08-10"), policy_timestep = 3) | 0.35
3 | 2019-03-10 | | inforce | (from = Date("2020-01-01"), to = Date("2020-03-09"), policy_timestep = 1) | 0.191667
3 | 2019-03-10 | | inforce | (from = Date("2020-03-10"), to = Date("2021-03-09"), policy_timestep = 2) | 1.0
3 | 2019-03-10 | | inforce | (from = Date("2021-03-10"), to = Date("2022-03-09"), policy_timestep = 3) | 1.0
3 | 2019-03-10 | | inforce | (from = Date("2022-03-10"), to = Date("2022-12-31"), policy_timestep = 4) | 0.808333
| **policy\_id**<br>`Int64` | **issue\_date**<br>`Date` | **end\_date**<br>`Date` | **status**<br>`String` | **policy\_year**<br>`@NamedTuple{from::Date, to::Date, policy\_timestep::Int64}` | **exposure\_fraction**<br>`Float64` |
|--------------------------:|--------------------------:|------------------------:|-----------------------:|---------------------------------------------------------------------------------:|------------------------------------:|
| 1 | 2020-05-10 | 2022-06-10 | claim | (from = Date("2020-05-10"), to = Date("2021-05-09"), policy\_timestep = 1) | 1.0 |
| 1 | 2020-05-10 | 2022-06-10 | claim | (from = Date("2021-05-10"), to = Date("2022-05-09"), policy\_timestep = 2) | 1.0 |
| 1 | 2020-05-10 | 2022-06-10 | claim | (from = Date("2022-05-10"), to = Date("2023-05-09"), policy\_timestep = 3) | 1.0 |
| 2 | 2020-04-05 | 2022-08-10 | lapse | (from = Date("2020-04-05"), to = Date("2021-04-04"), policy\_timestep = 1) | 1.0 |
| 2 | 2020-04-05 | 2022-08-10 | lapse | (from = Date("2021-04-05"), to = Date("2022-04-04"), policy\_timestep = 2) | 1.0 |
| 2 | 2020-04-05 | 2022-08-10 | lapse | (from = Date("2022-04-05"), to = Date("2022-08-10"), policy\_timestep = 3) | 0.35 |
| 3 | 2019-03-10 | 2022-12-31 | inforce | (from = Date("2020-01-01"), to = Date("2020-03-09"), policy\_timestep = 1) | 0.191667 |
| 3 | 2019-03-10 | 2022-12-31 | inforce | (from = Date("2020-03-10"), to = Date("2021-03-09"), policy\_timestep = 2) | 1.0 |
| 3 | 2019-03-10 | 2022-12-31 | inforce | (from = Date("2021-03-10"), to = Date("2022-03-09"), policy\_timestep = 3) | 1.0 |
| 3 | 2019-03-10 | 2022-12-31 | inforce | (from = Date("2022-03-10"), to = Date("2022-12-31"), policy\_timestep = 4) | 0.808333 |


## Discussion and Questions

Expand Down Expand Up @@ -274,4 +271,171 @@ And **not** like this:
(from = Date("2019-03-01"), to = Date("2020-02-28"), policy_timestep = 4)
(from = Date("2020-03-01"), to = Date("2021-02-29"), policy_timestep = 5)
...
```

## Example of Actual to Expected Analysis

```julia
# generate samples over a full leap cycle and
# show that we recover a ~100% A/E using a given
# assumption

println("------------------")
println("generating simulated experience")

using ExperienceAnalysis
using Dates
using DayCounts
using Distributions
using DataFramesMeta
using StableRNGs

rng = StableRNG(123)
q = 1 - (0.6)^(1 / (365.25 * 4)) # a daily rate for a risk that occurs ~0.1/year on average over a leap cycle

# simulate n policies and when they die using the above q
# set the end date for the study four years in, covering a whole leap cycle
# and presume we don't know data beyond that date
n = 1 * 10^6
years = 4
d_start = Date(2011, 1, 1)
d_end = d_start + Year(years) - Day(1)
census = map(1:n) do id
issue = rand(rng, d_start:Day(1):Dates.lastdayofyear(d_start))
death = issue + Day(rand(rng, Geometric(q)))
(; id, issue, death)

end |> DataFrame

# calculate (1, 2) grouped over pol/cal years and (3) total actual to expected

basis = [
ExperienceAnalysis.AnniversaryCalendar(Year(1), Year(1)),
ExperienceAnalysis.Calendar(Year(1)),
ExperienceAnalysis.Anniversary(Year(1))
]

for b in basis
@show b
cp = let cp = deepcopy(census) # copy to avoid messing with generated data

cp.exposures = exposure.(
b,
census.issue,
min.(d_end, census.death),
census.death .<= d_end;
study_end=d_end
)

cp = flatten(cp, :exposures)

# did claim happen before cutoff
cp.claim = map(cp.exposures, cp.death) do e, d
e.from <= d <= e.to
end

cp.exp_days = map(cp.exposures) do e
length(e.from:Day(1):e.to)
end
cp.expected = @. 1 - (1 - q)^cp.exp_days

cp.cal_year = map(cp.exposures) do e
year(e.from)
end

cp.pol_year = map(cp.exposures, cp.issue) do e, i
y = year(e.from)
if monthday(e.from) < monthday(i)
y -= 1
end
y
end

cp.exp_amt = map(cp.exposures) do e
yearfrac(e.from, e.to + Day(1), DayCounts.ActualActualISDA())
end
cp

end

# not needed for test, but demonstrates how to do cal/pol year grouping
summary = map([:pol_year, :cal_year]) do grouping
combine(groupby(cp, (grouping))) do gdf
exposures = sum(gdf.exp_amt)
claims = sum(gdf.claim)
expected = sum(gdf.expected)

q̂ = claims / exposures
ae = claims / expected

(; claims, expected, exposures, q̂, ae)
end
end


@show summary
@show sum(cp.claim) / sum(cp.expected), sum(cp.claim), sum(cp.expected), sum(cp.exp_days), sum(cp.exp_amt)
@test sum(cp.claim) / sum(cp.expected) ≈ 1.0 rtol = 5e-3
println("---------")
```

This produces the following output, showing an actual-to-expected result for three different exposure basis as well as being on a calendar and policy-year basis:

```
------------------
generating simulated experience
b = ExperienceAnalysis.AnniversaryCalendar{Year, Year}(Year(1), Year(1))
summary = DataFrame[4×6 DataFrame
Row │ pol_year claims expected exposures q̂ ae
│ Int64 Int64 Float64 Float64 Float64 Float64
─────┼────────────────────────────────────────────────────────────────
1 │ 2011 120715 1.20055e5 9.80143e5 0.123161 1.00549
2 │ 2012 104919 1.05409e5 8.60476e5 0.121931 0.995354
3 │ 2013 92578 92780.8 7.58434e5 0.122065 0.997814
4 │ 2014 41861 41870.8 3.42226e5 0.12232 0.999766, 4×6 DataFrame
Row │ cal_year claims expected exposures q̂ ae
│ Int64 Int64 Float64 Float64 Float64 Float64
─────┼────────────────────────────────────────────────────────────────
1 │ 2011 61471 61363.9 5.01539e5 0.122565 1.00174
2 │ 2012 112712 1.12714e5 9.18968e5 0.122651 0.999981
3 │ 2013 98760 98928.2 8.0869e5 0.122123 0.9983
4 │ 2014 87130 87109.4 7.12082e5 0.122359 1.00024]
(sum(cp.claim) / sum(cp.expected), sum(cp.claim), sum(cp.expected), sum(cp.exp_days), sum(cp.exp_amt)) = (0.9998814228722663, 360073, 360115.70148553397, 1074485834, 2.941279085822292e6)
---------
b = ExperienceAnalysis.AnniversaryCalendar{Nothing, Year}(nothing, Year(1))
summary = DataFrame[4×6 DataFrame
Row │ pol_year claims expected exposures q̂ ae
│ Int64 Int64 Float64 Float64 Float64 Float64
─────┼────────────────────────────────────────────────────────────────────
1 │ 2011 173896 1.73803e5 1.4376e6 0.120963 1.00054
2 │ 2012 98793 98977.4 826104.0 0.119589 0.998137
3 │ 2013 87161 87140.1 727311.0 0.11984 1.00024
4 │ 2014 223 230.637 1925.0 0.115844 0.966888, 4×6 DataFrame
Row │ cal_year claims expected exposures q̂ ae
│ Int64 Int64 Float64 Float64 Float64 Float64
─────┼─────────────────────────────────────────────────────────────────────
1 │ 2011 61471 61363.9 5.01539e5 0.122565 1.00174
2 │ 2012 112712 1.12735e5 938529.0 0.120094 0.999794
3 │ 2013 98760 98942.2 825817.0 0.119591 0.998158
4 │ 2014 87130 87109.7 727057.0 0.119839 1.00023]
(sum(cp.claim) / sum(cp.expected), sum(cp.claim), sum(cp.expected), sum(cp.exp_days), sum(cp.exp_amt)) = (0.9997833363330586, 360073, 360151.03164316854, 1093362393, 2.9929420931506846e6)
---------
b = ExperienceAnalysis.AnniversaryCalendar{Year, Nothing}(Year(1), nothing)
summary = DataFrame[4×6 DataFrame
Row │ pol_year claims expected exposures q̂ ae
│ Int64 Int64 Float64 Float64 Float64 Float64
─────┼─────────────────────────────────────────────────────────────────────
1 │ 2011 120715 1.20069e5 1.00093e6 0.120603 1.00538
2 │ 2012 104919 1.05392e5 8.78469e5 0.119434 0.99551
3 │ 2013 92578 92777.8 774366.0 0.119553 0.997846
4 │ 2014 41861 43496.8 3.5624e5 0.117508 0.962393, 4×6 DataFrame
Row │ cal_year claims expected exposures q̂ ae
│ Int64 Int64 Float64 Float64 Float64 Float64
─────┼─────────────────────────────────────────────────────────────────────
1 │ 2011 120715 1.20069e5 1.00093e6 0.120603 1.00538
2 │ 2012 104919 1.05392e5 8.78469e5 0.119434 0.99551
3 │ 2013 92578 92777.8 774366.0 0.119553 0.997846
4 │ 2014 41861 43496.8 3.5624e5 0.117508 0.962393]
(sum(cp.claim) / sum(cp.expected), sum(cp.claim), sum(cp.expected), sum(cp.exp_days), sum(cp.exp_amt)) = (0.9954028354972483, 360073, 361735.9597133631, 1099590758, 3.01000275415076e6)
---------
```
2 changes: 1 addition & 1 deletion test/experience_machine.jl
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Original file line number Diff line number Diff line change
@@ -1,5 +1,5 @@
@testset "Generated Experience" begin
# generate samples over a fully leap cycle and
# generate samples over a full leap cycle and
# ensure that we can recover a ~100% A/E using a given
# assumption

Expand Down

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