BerquistSherman

class chainladder.BerquistSherman(paid_amount=None, incurred_amount=None, reported_count=None, closed_count=None, trend=0.0, reported_count_estimator=None)

Class to alter the inner diagonals of a Triangle using the methods described by Berquist and Sherman.

Parameters:

paid_amount: str

The triangle column associated with paid amounts

incurred_amount: str

The triangle column associated with incurred amounts

reported_count: str

The triangle column associated with reported claim count

closed_count: str

The triangle column associated with closed claim counts

trend: float (default=0.0)

Trend rate underlying average open case reserves.

reported_count_estimator: Estimator

An IBNR estimator for reported_count used to calculate closed_count disposal rates. Estimator can be a Pipeline. If None selected then basic Chainladder model is used.

Attributes:

adjusted_triangle_: Triangle

A set of triangles represented by each simulation

disposal_rate_: Triangle

The disposal rates of closed claims based on the reported_count_estimator

a_: Triangle

Two-period Exponential intercept parameters

b_: Triangle

Two-period Exponential slope parameters

Examples

trend tilts the case-adequacy adjustment before Incurred is rebuilt; on the MedMal slice the inner diagonals of the adjusted Incurred triangle restate materially between 0% and 15% annual drift, while the latest diagonal is preserved.

tri = cl.load_sample("berqsherm").loc["MedMal"]
base = cl.BerquistSherman(
    paid_amount="Paid",
    incurred_amount="Incurred",
    reported_count="Reported",
    closed_count="Closed",
    trend=0.0,
).fit(tri)
tilted = cl.BerquistSherman(
    paid_amount="Paid",
    incurred_amount="Incurred",
    reported_count="Reported",
    closed_count="Closed",
    trend=0.15,
).fit(tri)
print(np.round(base.adjusted_triangle_["Incurred"], 0))

              12          24          36          48          60          72          84          96
1969   9883293.0  27420103.0  35879085.0  43105257.0  33438702.0  30397324.0  25723694.0  23506000.0
1970   8641763.0  31305782.0  41543535.0  48550616.0  38203864.0  36222888.0  32216000.0         NaN
1971  11733960.0  43887171.0  61649896.0  64917222.0  51410209.0  48377000.0         NaN         NaN
1972  13638651.0  50987209.0  66696278.0  72777529.0  61163000.0         NaN         NaN         NaN
1973  14387930.0  45470590.0  56577593.0  73733000.0         NaN         NaN         NaN         NaN
1974  13630366.0  47189379.0  63477000.0         NaN         NaN         NaN         NaN         NaN
1975  15036351.0  48904000.0         NaN         NaN         NaN         NaN         NaN         NaN
1976  15791000.0         NaN         NaN         NaN         NaN         NaN         NaN         NaN

print(np.round(tilted.adjusted_triangle_["Incurred"], 0))

              12          24          36          48          60          72          84          96
1969   3793504.0  12084942.0  18563821.0  25924316.0  23516364.0  24979245.0  24016864.0  23506000.0
1970   3760482.0  15830500.0  24615996.0  33169802.0  30722141.0  33362729.0  32216000.0         NaN
1971   5982185.0  25583831.0  41384825.0  50323342.0  46191356.0  48377000.0         NaN         NaN
1972   7819355.0  33794110.0  51361061.0  64559286.0  61163000.0         NaN         NaN         NaN
1973   9533246.0  34585431.0  49667342.0  73733000.0         NaN         NaN         NaN         NaN
1974  10348458.0  41241243.0  63477000.0         NaN         NaN         NaN         NaN         NaN
1975  13102479.0  48904000.0         NaN         NaN         NaN         NaN         NaN         NaN
1976  15791000.0         NaN         NaN         NaN         NaN         NaN         NaN         NaN

fit(X, y=None, sample_weight=None)

set_params(**params)

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as Pipeline). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Parameters:

**paramsdict

Estimator parameters.

Returns:

selfestimator instance

Estimator instance.

transform(X)

If X and self are of different shapes, align self to X, else return self.

Parameters:

X: Triangle

The triangle to be transformed

Returns:

X_new: New triangle with transformed attributes.

Inherited Methods

BerquistSherman.fit_transform	Fit to data, then transform it.
BerquistSherman.get_metadata_routing	Get metadata routing of this object.
BerquistSherman.get_params	Get parameters for this estimator.
BerquistSherman.set_output	Set output container.
BerquistSherman.to_json	Serializes triangle object to json format
BerquistSherman.to_pickle	Serializes triangle object to pickle.