---
title: "Why datey?"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Why datey?}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
```

```{r setup}
library(datey)
```

## The unit is years, but the data are dates

Mortality rates, valuation assumptions and many other actuarial quantities are
defined *per year*. The data they are applied to -- dates of birth, dates of
death, policy anniversaries, valuation dates -- are measured in days.

Converting between the two seems like it should be trivial, but it isn't. Consider these calculations:

- "Add one year" to 2024&#x2011;02&#x2011;29. There is no
2025&#x2011;02&#x2011;29, so is it 2025&#x2011;02&#x2011;28
or is it 2025&#x2011;03&#x2011;01? Both are defensible, and different tools (and
different people) choose differently.

- "Add half a year" twice starting from 2000&#x2011;01&#x2011;01. Does this
land on the same point in time as a single "add one year" step? With most day-based
arithmetic, the answer is no -- the result depends on how you split the
year up, and on the order in which you do the additions.

For a single *ad hoc* calculation this kind of ambiguity is a curiosity. For an
actuarial model that combines exposure periods, runs sensitivities, and is
reconciled and audited, it's a problem: the same logical calculation,
expressed two different but equivalent ways, can produce two different
numbers.

## The **datey** approach: a fixed annual grid

**datey** picks *one* standardised, precise mapping from dates onto
an annual grid, and guarantees that arithmetic on that grid is exact and
associative. Every `datey` and `durationy` is stored internally as a count of
*clicks*, where one click is 1&#8201;/&#8201;534&#8201;360 of a year,
a number chosen so that 1/365 and 1/366 of a year, and useful fractions of days and years, are 
represented exactly.

With this approach, date and duration calculations
reduce to plain old integer arithmetic which is both precise and associative.

The practical consequence is that the two-steps-vs-one-step problem above
does not arise:

```{r}
start <- start_day(2000, 1, 1)

half_year <- durationy(0.5)
two_steps <- (start + half_year) + half_year
one_step  <- start + (half_year + half_year)

two_steps
one_step
identical(two_steps, one_step)
```

`(a + d1) + d2 == a + (d1 + d2)` for any `datey` `a` and `durationy`s `d1`,
`d2` -- always, exactly, regardless of leap years or the order of operations.
That's the guarantee **datey** is built around, and the [specification][spec]
sets it out precisely.

## Interval algebra for rate periods

Actuarial calculations very often involve asking "for how much of this period
did rate X apply?" -- e.g. combining a policy's time at risk with the period
over which a particular assumption set is valid.

**datey** represents time intervals as `datey_interval`s, written `start %to% end`.
These are half-open, i.e. `[start, end)`, intervals, which means consecutive 
periods interlock precisely without gaps or double-counting.

**datey** provides interval algebra to work with time intervals directly:

```{r}
time_at_risk <- start_day(2023, 4, 1) %to% end_day(2024, 4, 1)
rate_period_2024 <- start_day(2024, 1, 1) %to% end_day(2025, 12, 31)

# the part of the time at risk to which the 2024 rate applies
overlap <- time_at_risk & rate_period_2024
overlap

# ... as a duration in years, ready to multiply by an annual rate
durationy(overlap$end - overlap$start)
```

## Standardised day-fractions for exposure calculations

Because a `datey` can represent a position *within* a day (as a fraction of a
year), **datey** provides `start_day()`, `mid_day()` and `end_day()` for the three
points within a day that come up most often:

- `start_day()` -- the day is *included* from its start. Use this e.g.
  for the start of a period at risk.
- `end_day()` -- the day is included up to and including its end. This is often
  how the end of risk periods are specified.
- `mid_day()` -- on average, an event such as death occurs halfway through the
  day it is recorded on.

Choosing consistently between these (rather than, say, always using midnight)
improves clarity and accuracy as to what events are and are not included in a
time period.

```{r}
y <- 2026L
m <- 1L
d <- 1L
one_day_period <- start_day(y, m, d) %to% end_day(2026, m, d)
one_day_period

mid <- mid_day(y, m, d)
mid

interval_includes(one_day_period, mid)
```

## What **datey** deliberately leaves out

To keep the guarantees above simple and dependable, **datey** is very narrowly scoped.
It is *not* the right tool for:

- General date arithmetic for output, e.g. "what date is 3 months from now"
  for a calendar shown to a user.
- Parsing or formatting dates beyond the simple
  `YYYY-MM-DD[.fff]` representation.
- Time zones, daylight saving time, leap seconds, or different calendars.

Packages like [clock](https://clock.r-lib.org/) and
[lubridate](https://lubridate.tidyverse.org/) already do that.

The trade-off is deliberate: by refusing to be a general date library, **datey**
can make a precise, associative annual grid *the* representation for
rate-related calculations, with one well-defined answer regardless of how the
calculation is structured.

[spec]: spec.html
