MackChainladder

MackChainladder#

class chainladder.MackChainladder[source]#

Basic stochastic chainladder method popularized by Thomas Mack

Parameters:

None

Attributes:

X_:: returns X
ultimate_:: The ultimate losses per the method
ibnr_:: The IBNR per the method
full_expectation_:: The ultimates back-filled to each development period in X replacing the known data
full_triangle_:: The ultimates back-filled to each development period in X retaining the known data
summary_:: summary of the model
full_std_err_:: The full standard error
total_process_risk_:: The total process error
total_parameter_risk_:: The total parameter error
mack_std_err_:: The total prediction error by origin period
total_mack_std_err_:: The total prediction error across all origin periods

Examples

Use MackChainladder when the IBNR point estimate alone is not sufficient and a measure of reserve uncertainty is also needed. summary_ shows the deterministic chainladder ultimate alongside Mack’s per-origin prediction error.

tr = cl.load_sample('ukmotor')
model = cl.MackChainladder().fit(tr)
print(model.summary_)

       Latest          IBNR      Ultimate  Mack Std Err
12690.0           NaN  12690.000000           NaN
12746.0    350.902024  13096.902024     27.246756
12993.0   1037.536767  14030.536767     36.524408
11093.0   2044.859861  13137.859861    144.534287
10217.0   3663.404483  13880.404483    427.634355
 9650.0   7162.150646  16812.150646    693.166178
 6283.0  14396.919151  20679.919151    901.408385

total_mack_std_err_ aggregates the prediction error across all origins. It exceeds the quadrature sum of the per-origin errors in summary_ because parameter risk is correlated across origins: all origins share the same estimated age-to-age factors.

print(model.total_mack_std_err_)

columns        values
(Total,)  1424.531543

The Mack standard error is sensitive to how the upstream development factors were estimated. Using simple (unweighted) averaging in Development before fitting MackChainladder gives equal weight to each accident year regardless of size. On a small triangle this raises the aggregate standard error relative to volume weighting, since thinner years contribute more uncertainty.

tr = cl.load_sample("ukmotor")
tr_simple = cl.Development(average="simple").fit_transform(tr)
print(cl.MackChainladder().fit(tr_simple).total_mack_std_err_)

columns        values
(Total,)  1591.603339

fit(X, y=None, sample_weight=None)[source]#

Fit the model with X.

Parameters:

X: Triangle-like: Data to which the model will be applied.
y: Ignored
sample_weight: Ignored

Returns:

self: object: Returns the instance itself.

Examples

After fitting, ibnr_ holds the point estimate per origin and mack_std_err_ holds the prediction error. The ratio of the two gives a coefficient of variation that shows which origins carry the most reserve uncertainty relative to their size.

import numpy as np
import pandas as pd

tr = cl.load_sample('ukmotor')
model = cl.MackChainladder().fit(tr)
df = model.ibnr_.to_frame(origin_as_datetime=False).round(1)
df.columns = ["IBNR"]
df["Mack Std Err"] = np.round(
    model.mack_std_err_.values[0, 0, :, -1], 1
)
print(df)

         IBNR  Mack Std Err
    NaN           NaN
  350.9          27.2
 1037.5          36.5
 2044.9         144.5
 3663.4         427.6
 7162.2         693.2
14396.9         901.4

predict(X, sample_weight=None)[source]#

Predicts the Mack chainladder ultimate on a new triangle X.

The fitted age-to-age factors and sigma estimates from self.X_ are applied to X to compute ultimate_ and the Mack standard errors (parameter risk, process risk, mack_std_err_, total_mack_std_err_) on the predicted Triangle.

Parameters:

X: Triangle: Loss data to which the fitted model will be applied. Must share the same shape as the Triangle used in fit().
sample_weight: Triangle: Optional exposure used in CDF alignment.

Returns:

X_new: Triangle: Triangle with ultimate_ and Mack std error attributes attached.

Examples

predict re-applies the fitted age-to-age factors and sigma estimates to a new triangle without refitting. A common use is sensitivity testing: hold the development pattern fixed and scale the reported losses by an adverse factor to see how the Mack standard error responds. Under Mack (1993), the prediction error scales approximately proportionally with the reserve level because sigma is estimated from the original fit and held fixed; applying the factors to a uniformly scaled triangle would give exactly proportional results, but scaling only the reported diagonal (as below) gives a slightly smaller increase.

tr = cl.load_sample('ukmotor')
model = cl.MackChainladder().fit(tr)
tr_adverse = tr * 1.05
print(model.predict(tr).total_mack_std_err_)
print(model.predict(tr_adverse).total_mack_std_err_)

columns        values
(Total,)  1424.531543
columns        values
(Total,)  1475.539173

Inherited Methods

`MackChainladder.fit_predict`
`MackChainladder.get_metadata_routing`	Get metadata routing of this object.
`MackChainladder.get_params`	Get parameters for this estimator.
`MackChainladder.intersection`	Given two Triangles with mismatched indices, this method aligns their indices
`MackChainladder.pipe`	Apply `func(self, args, *kwargs)`.
`MackChainladder.set_backend`	Converts triangle array_backend.
`MackChainladder.set_params`	Set the parameters of this estimator.
`MackChainladder.to_json`	Serializes triangle object to json format
`MackChainladder.to_pickle`	Serializes triangle object to pickle.
`MackChainladder.validate_X`
`MackChainladder.validate_weight`

MackChainladder

Contents

MackChainladder#