reserving.CapeCod

The Cape Cod (Stanard–Bühlmann) method: Bornhuetter–Ferguson with each

Usage

reserving.CapeCod()

origin’s apriori estimated from the triangle, as chainladder-python’s CapeCod.

Origin j’s used-up exposure is exposure[j] / cdf[j] and its latest value is trended to the triangle’s valuation by (1 + trend) ** (months / 12), the months running from the end of the origin period. Origin i’s trended apriori is the sum of the trended latest values weighted by decay ** abs(i - j) over the same weighted sum of used-up exposures; dividing by its own trend factor gives the apriori of its Bornhuetter–Ferguson ultimate.

Parameters

trend: float = 0.0: Annual trend of the loss ratio; above -1.
decay: float = 1.0: Weight of an origin n periods away, decay ** n; from 0 to 1. With 1 every origin shares one loss ratio.
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 CapeCod, 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 = CapeCod().fit(tri, "paid", "premium")
>>> [round(a, 4) for a in fit.apriori], [round(u, 2) for u in fit.ultimate]

([0.6774, 0.6774], [150.0, 290.32])

Attributes

Name	Description
average	How link ratios are averaged.
decay	Weight of an origin one period away.
sigma_interpolation	How unestimable variance parameters are filled in.
tail	The tail: a constant factor as a number, otherwise its estimator.
trend	Annual trend of the loss ratio.

average

How link ratios are averaged.

average: str

decay

Weight of an origin one period away.

decay: float

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

trend

Annual trend of the loss ratio.

trend: float

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 and apriori. Trend runs to the triangle’s valuation.

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

CapeCodFit

Raises

ValueError: As ChainLadder.fit, if trend or decay is out of range, or if an origin has no observed, finite, positive exposure.