reserving.Benktander

The Benktander (iterated Bornhuetter–Ferguson) method: starting from

Usage

reserving.Benktander()

U(0) = apriori * exposure, U(k) = latest + (1 - 1 / cdf) * U(k-1) for n_iters steps, as chainladder-python’s Benktander. n_iters=0 is the expected loss method, 1 is Bornhuetter–Ferguson, and many iterations approach the chain ladder. The steps are summed in closed form, so a large n_iters is cheap; where an origin’s cdf is below 1/2 they diverge instead.

Parameters

apriori: float = 1.0

Expected loss ratio of the starting ultimate; positive.

n_iters: int = 1

Number of Bornhuetter–Ferguson steps.

average: (volume, simple, regression) = "volume"

How link ratios are averaged, as in ChainLadder.

sigma_interpolation: (log - linear, mack) = "log-linear"
tail: (float, TailConstant, TailCurve, TailBondy or TailLogLinear)
As ChainLadder; no tail by default.

Examples

>>> from prospicio.reserving import Benktander, Triangle
>>> tri = Triangle.from_long(
...     [2020, 2020, 2021], [12, 24, 12],
...     {"paid": [100.0, 150.0, 200.0], "premium": [250.0, 250.0, 400.0]},
... )
>>> fit = Benktander(apriori=0.5, n_iters=2).fit(tri, "paid", "premium")
>>> [round(u, 2) for u in fit.ultimate]

[150.0, 288.89]

Attributes

Name Description
apriori Expected loss ratio of the starting ultimate.
average How link ratios are averaged.
n_iters Number of Bornhuetter–Ferguson steps.
sigma_interpolation How unestimable variance parameters are filled in.
tail The tail: a constant factor as a number, otherwise its estimator.

apriori

Expected loss ratio of the starting ultimate.

apriori: float

average

How link ratios are averaged.

average: str

n_iters

Number of Bornhuetter–Ferguson steps.

n_iters: int

sigma_interpolation

How unestimable variance parameters are filled in.

sigma_interpolation: str

tail

The tail: a constant factor as a number, otherwise its estimator.

tail: Any

Methods

Name Description
fit() Fits one loss column in every segment of a triangle, each with its

fit()

Fits one loss column in every segment of a triangle, each with its

Usage

fit(triangle, column, exposure)

own exposure.

Parameters
triangle: Triangle
column: str

The losses to project.

exposure: str
The exposure column; each origin’s latest observed cumulative value is its exposure (an incremental triangle’s is cumulated).
Returns
ExpectedLossFit
Raises
ValueError
As ExpectedLoss.fit.