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actxps maintainer (mattheaphy/actxps#23) and SOA experience studies document indicate that not including partial exposures on left truncation is standard practice. Asking in linked issue about right truncation as well.

update: in linked issue the approach taken by actxps is to not include left truncation intervals but to include right truncation intervals. Not entirely sure of the consistency of these things. Maybe some simulated scenarios can help understand these things without going through the math. Or maybe going through the math is necessary. A bit unsure.

update 2: seems to be consistent with the advice from section 17.6.4 of experience studies document.

https://www.actuarialopensource.org/actxps_experienceanalysis_2023_02_03.html#jl-dup

How to interpret dates in this package?

suppose we get this result from exposure function

[(from = Date("2016-07-04"), to = Date("2017-07-04")), (from = Date("2017-07-04"), to = Date("2017-07-05"))]

because res[1].to == res[2].from, I assume that they both refer to the same time on the clock (midnight?) so that there is no overlap. But if we get this result

[(from = Date("2016-07-04"), to = Date("2016-07-04"))]

then the interval of time represented by it contains only a single instant and has exposure of 0?

I propose an alternative -

How I would like to do it

first result

[(from = Date("2016-07-04"), to = Date("2017-07-03")), (from = Date("2017-07-04"), to = Date("2017-07-05"))]

second result

[(from = Date("2016-07-04"), to = Date("2016-07-04"))]

interpretation

supposing we have implemented study_start and study_end

How I interpret inputs -

• issue is the Dates.Date containing the Dates.Instant where the policy was issued
• termination is the Dates.Date containing the Dates.Instant where the policy was terminated
• study_start includes the entire day, starts at midnight
• study_end includes the entire day, ends at 23:59.9999... military time

How I interpret the outputs -

• tuple.from is the beginning of the date interval. How does this relate to the Date.Instant where policy is issued?
  • If issue < study_start then the first interval's tuple.from refers to midnight/beginning of day, so that the entire day is included.
  • If issue >= study_start then the first interval's tuple.from might most accurately be a Dates.Instant, but we simplify things by allowing tuple.from to start at midnight, so that there is a full exposure and that we are consistent with our other case.
• tuple.to is the end of the date interval. How does this relate to the Date.Instant where policy is terminated or where the study ends?
  • if study_end < termination then we suppose that the study_end means we should include the entire day of study_end and the Dates.Instant of tuple.to is at 23:59.999 military time.
  • if study_end >= termination then the termination happens at some time during this day, but we simplify by allowing tuple.to to end at 23:59.999.

In this interpretation the simplification causes some error, maybe some analysis should be done to estimate or put bounds on this error. Maybe this is done in that document from the SOA linked in the description.

exposure(Anniversary(Month(1)), Date(2013, 1, 31), Date(2012, 4, 1))

gives

1-element Vector{NamedTuple{(:from, :to), Tuple{Date, Date}}}:
 (from = Date("2013-01-31"), to = Date("2012-04-01"))

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https://www.actuarialopensource.org/actxps_experienceanalysis_2023_02_03.html#leap

Thinking about an API that just returns an iterator of dates for the partitions.

Think it can be faster than pushing to array? Also maybe less opinionated than doing the NamedTuple with from and to.

https://www.actuarialopensource.org/actxps_experienceanalysis_2023_02_03.html#term-is-anniv

We have code like

struct Anniversary{T} <: ExposurePeriod
    pol_period::T
end

but I think it should be something like

struct Anniversary <: ExposurePeriod
    pol_period::Period
end

and probably even as strict as

struct Anniversary <: ExposurePeriod
    pol_period::DatePeriod
end

I don't think there it necessary to operate at any granularity finer than a single day, so I am going to be using DatePeriod instead of Period in a PR.

reproduction

using ExperienceAnalysis
using Dates

exposure(ExperienceAnalysis.Calendar(Year(1)), Date(2006,6,15), Date(2020,2,29), true) # works
exposure(ExperienceAnalysis.Calendar(Hour(1)), Date(2006,6,15), Date(2020,2,29), true) # ERROR: MethodError: no method matching floor(::Date, ::Hour)

This is because floor of date only works for DatePeriod

It isn't clear how I am to get the policy year from an exposure interval

Currently, exposures(basis,from,to,continued_exposure=false) uses the from argument as the anchor point for anniversaries. Refactor to allow the study start to be incorporated? Currently process is a little clunky.

Alternative API could be: exposure(basis,anniv_date,termination_date,study_start,study_end,continued_exposure=false)

This is also not ideal because termination_date could be a date, or nothing, or missing or however user has data stored. Perhaps enforce that it must be a date or nothing?

Brainstorm ideas for built-in functionality here (or open new, separate issue)

Seems like just indicating that the interval is the final interval and contains the decrement we are analyzing will work. I am not sure how continued_exposure will work for AnniversaryCalendar. The equation is probably like $\frac{events}{exposures}$?