reserving.ClaimsDevelopmentResult

Merz and Wüthrich’s (2008) one-year view of a Mack fit: standard errors

Usage

reserving.ClaimsDevelopmentResult()

of the claims development result (CDR), the change in the chain-ladder ultimate over a calendar year, per origin and in total. The total includes the covariance between origins. Year k of the run-off is R ChainLadder’s CDR(k)S.E.; summed in square over the years, the run-off gives back Mack’s standard error.

Examples

>>> from prospicio.reserving import Mack, Triangle
>>> tri = Triangle.from_long(
...     [2020] * 4 + [2021] * 3 + [2022] * 2 + [2023],
...     [12, 24, 36, 48, 12, 24, 36, 12, 24, 12],
...     [100.0, 150.0, 165.0, 170.0, 110.0, 170.0, 180.0, 120.0, 175.0, 130.0],
... )
>>> mack = Mack().fit(tri, "values")
>>> cdr = mack.claims_development_result()
>>> len(cdr.by_calendar_year), cdr.one_year_standard_error[0]

(3, 0.0)

>>> abs(cdr.total_run_off_standard_error - mack.total_standard_error) < 1e-9

True

Attributes

Name	Description
by_calendar_year	Standard error of each origin’s CDR in each future calendar year:
one_year_standard_error	Standard error of each origin’s CDR in the next calendar year, R’s
origins	Origin periods, oldest first.
run_off_standard_error	Standard error of each origin’s full run-off, the square root of
total_by_calendar_year	Standard error of the total CDR in each future calendar year.
total_one_year_standard_error	Standard error of the total CDR in the next calendar year.
total_run_off_standard_error	Standard error of the total full run-off; equals Mack’s.

by_calendar_year

Standard error of each origin’s CDR in each future calendar year:

by_calendar_year: list[list[float]]

by_calendar_year[k - 1][i] is year k (R’s CDR(k)S.E.) of origin i, zero once the origin is fully developed. One year per age-to-age factor.

one_year_standard_error

Standard error of each origin’s CDR in the next calendar year, R’s

one_year_standard_error: list[float]

CDR(1)S.E..

origins

Origin periods, oldest first.

origins: list[str]

run_off_standard_error

Standard error of each origin’s full run-off, the square root of

run_off_standard_error: list[float]

the sum of its yearly mean squared errors; equals Mack’s.

total_by_calendar_year

Standard error of the total CDR in each future calendar year.

total_by_calendar_year: list[float]

total_one_year_standard_error

Standard error of the total CDR in the next calendar year.

total_one_year_standard_error: float

total_run_off_standard_error

Standard error of the total full run-off; equals Mack’s.

total_run_off_standard_error: float

Methods

Name	Description
to_frame()	One row per origin: `origin`, then `cdr_1`, `cdr_2`, … the

to_frame()

One row per origin: origin, then cdr_1, cdr_2, … the

Usage

to_frame()

standard error of the CDR in each future calendar year (R’s CDR(k)S.E.), and run_off, that of the full run-off. Needs pandas.

Returns

pandas.DataFrame