Development

Development#

class chainladder.Development(n_periods: int = -1, average: Literal['volume', 'simple', 'regression', 'geometric'] = 'volume', sigma_interpolation: Literal['log-linear', 'mack'] = 'log-linear', drop: tuple | list[tuple] | None = None, drop_high: bool | int | list[bool] | list[int] | None = None, drop_low: bool | int | list[bool] | list[int] | None = None, preserve: int = 1, drop_valuation: str | list[str] = None, drop_above: float = inf, drop_below: float = 0.0, fillna: float | None = None, groupby: Callable | list | str | Series = None)[source]#

A Transformer that allows for basic loss development pattern selection.

Parameters:
n_periods: integer, optional (default = -1)

number of origin periods to be used in the ldf average calculation. For all origin periods, set n_periods = -1

average: literal (or list of literals), or float, optional (default = ‘volume’)

type of averaging to use for ldf average calculation. Options include ‘volume’, ‘simple’, ‘regression’, and ‘geometric’. If numeric values are supplied, then (2-average) in the style of Zehnwirth & Barnett is used for the exponent of the regression weights.

sigma_interpolation: string optional (default = ‘log-linear’)

Options include ‘log-linear’ and ‘mack’

drop: tuple or list of tuples

Drops specific origin/development combination(s). See order of operations below when combined with multiple drop parameters.

drop_high: bool, int, list of bools, or list of ints (default = None)

Drops highest (by rank) link ratio(s) from LDF calculation If a boolean variable is passed, drop_high is set to 1, dropping only the highest value. Protected by preserve. See order of operations below when combined with multiple drop parameters.

drop_low: bool, int, list of bools, or list of ints (default = None)

Drops lowest (by rank) link ratio(s) from LDF calculation If a boolean variable is passed, drop_low is set to 1, dropping only the lowest value. Protected by preserve. See order of operations below when combined with multiple drop parameters.

drop_above: float or list of floats (default = numpy.inf)

Drops all link ratio(s) above the given parameter from the LDF calculation. Protected by preserve. See order of operations below when combined with multiple drop parameters.

drop_below: float or list of floats (default = 0.00)

Drops all link ratio(s) below the given parameter from the LDF calculation. Protected by preserve. See order of operations below when combined with multiple drop parameters.

preserve: int (default = 1)

The minimum number of link ratio(s) required for LDF calculation. See order of operations below when combined with multiple drop parameters.

drop_valuation: str or list of str (default = None)

Drops specific valuation periods. str must be date convertible. See order of operations below when combined with multiple drop parameters.

fillna: float, (default = None)

Used to fill in zero or nan values of an triangle with some non-zero amount. When an link-ratio has zero as its denominator, it is automatically excluded from the ldf_ calculation. For the specific case of ‘volume’ averaging in a deterministic method, this may be reasonable. For all other averages and stochastic methods, this assumption should be avoided.

groupby: Callable, list, str, Series (default = None)

An option to group levels of the triangle index together for the purposes of estimating patterns. If omitted, each level of the triangle index will receive its own patterns.

Note

(Order of Drop Operations)

When multiple drop parameters are used together, the weights are built in this order:

  1. n_periods — limit to the most recent origin periods.

  2. drop — remove specific origin/development cells.

  3. drop_valuation — remove entire valuation diagonal in the triangle.

  4. drop_high / drop_low — remove highest/lowest link ratios by rank (eligible factors from n_periods are used; protected by preserve, which may relax exclusions from this step if too few ratios would remain then this step is skipped).

  5. drop_above / drop_below — remove link ratios outside a range (Protected by``preserve``, which may relax exclusions from this step if too few ratios would remain then this step is skipped).

  6. Calculate the loss development factors using average method.

Attributes:
ldf_: Triangle

The estimated loss development patterns

cdf_: Triangle

The estimated cumulative development patterns

sigma_: Triangle

Sigma of the ldf regression

std_err_: Triangle

Std_err of the ldf regression

std_residuals_: Triangle

A Triangle representing the weighted standardized residuals of the estimator as described in Barnett and Zehnwirth.

Examples

There are lots of parameters to control the development pattern selection. One should exercise caution when multiple drop parameters are used together.

Let’s start with a triangle and inspect its link ratios.

tri = cl.load_sample("xyz")
print(tri["Incurred"].link_ratio)

         12-24     24-36     36-48     48-60     60-72     72-84     84-96    96-108   108-120   120-132
1998       NaN       NaN  1.108227  1.067528  1.064392  1.044146  1.114243  0.987596  0.979707  0.999179
1999       NaN  1.237646  1.197135  1.144305  1.057447  1.055967  0.988085  1.011131  1.001436       NaN
2000  1.196032  1.168062  1.239452  1.086354  1.168543  1.072291  1.015048  0.993094       NaN       NaN
2001  1.353175  1.313547  1.264295  1.286967  1.085689  1.037834  1.006668       NaN       NaN       NaN
2002  1.590040  1.308591  1.413078  1.179122  1.096524  0.989076       NaN       NaN       NaN       NaN
2003  1.760957  1.786055  1.337353  1.089595  1.003210       NaN       NaN       NaN       NaN       NaN
2004  2.364225  1.465057  1.218140  0.980211       NaN       NaN       NaN       NaN       NaN       NaN
2005  1.654181  1.482965  1.004478       NaN       NaN       NaN       NaN       NaN       NaN       NaN
2006  1.728479  1.043199       NaN       NaN       NaN       NaN       NaN       NaN       NaN       NaN
2007  1.629204       NaN       NaN       NaN       NaN       NaN       NaN       NaN       NaN       NaN

We can drop a specific origin/development combination by passing a tuple to the drop parameter. By using the fit_transform method, we can see the link ratios after the drop.

print(cl.Development(drop=("2004", 12)).fit_transform(tri["Incurred"]).link_ratio)

         12-24     24-36     36-48     48-60     60-72     72-84     84-96    96-108   108-120   120-132
1998       NaN       NaN  1.108227  1.067528  1.064392  1.044146  1.114243  0.987596  0.979707  0.999179
1999       NaN  1.237646  1.197135  1.144305  1.057447  1.055967  0.988085  1.011131  1.001436       NaN
2000  1.196032  1.168062  1.239452  1.086354  1.168543  1.072291  1.015048  0.993094       NaN       NaN
2001  1.353175  1.313547  1.264295  1.286967  1.085689  1.037834  1.006668       NaN       NaN       NaN
2002  1.590040  1.308591  1.413078  1.179122  1.096524  0.989076       NaN       NaN       NaN       NaN
2003  1.760957  1.786055  1.337353  1.089595  1.003210       NaN       NaN       NaN       NaN       NaN
2004       NaN  1.465057  1.218140  0.980211       NaN       NaN       NaN       NaN       NaN       NaN
2005  1.654181  1.482965  1.004478       NaN       NaN       NaN       NaN       NaN       NaN       NaN
2006  1.728479  1.043199       NaN       NaN       NaN       NaN       NaN       NaN       NaN       NaN
2007  1.629204       NaN       NaN       NaN       NaN       NaN       NaN       NaN       NaN       NaN

We can also inspect the LDFs with the ldf_ property.

ldf = cl.Development(drop=("2004", 12)).fit(tri["Incurred"]).ldf_
print(ldf)

          12-24     24-36     36-48     48-60     60-72     72-84     84-96    96-108   108-120   120-132
(All)  1.582216  1.339353  1.193406  1.095906  1.076968  1.033612  1.019016  0.997636  0.992918  0.999179

We can also drop all link ratio(s) above the given parameter by passing a list of floats to the drop_above parameter. Let’s inspect the link ratios after the drop.

tri = cl.load_sample("xyz")
print(
    cl.Development(drop_above=[2.0, 1.5, 1.3, 1.2, 1.1, 1.07, 1.05, 1.03, 1.01, 1.00])
    .fit_transform(tri["Incurred"])
    .link_ratio
)

         12-24     24-36     36-48     48-60     60-72     72-84     84-96    96-108   108-120   120-132
1998       NaN       NaN  1.108227  1.067528  1.064392  1.044146       NaN  0.987596  0.979707  0.999179
1999       NaN  1.237646  1.197135  1.144305  1.057447  1.055967  0.988085  1.011131  1.001436       NaN
2000  1.196032  1.168062  1.239452  1.086354       NaN       NaN  1.015048  0.993094       NaN       NaN
2001  1.353175  1.313547  1.264295       NaN  1.085689  1.037834  1.006668       NaN       NaN       NaN
2002  1.590040  1.308591       NaN  1.179122  1.096524  0.989076       NaN       NaN       NaN       NaN
2003  1.760957       NaN       NaN  1.089595  1.003210       NaN       NaN       NaN       NaN       NaN
2004       NaN  1.465057  1.218140  0.980211       NaN       NaN       NaN       NaN       NaN       NaN
2005  1.654181  1.482965  1.004478       NaN       NaN       NaN       NaN       NaN       NaN       NaN
2006  1.728479  1.043199       NaN       NaN       NaN       NaN       NaN       NaN       NaN       NaN
2007  1.629204       NaN       NaN       NaN       NaN       NaN       NaN       NaN       NaN       NaN

Then, let the LDFs.

tri = cl.load_sample("xyz")
ldf = (
    cl.Development(drop_above=[2.0, 1.5, 1.3, 1.2, 1.1, 1.07, 1.05, 1.03, 1.01, 1.00])
    .fit(tri["Incurred"])
    .ldf_
)
print(ldf)

          12-24     24-36     36-48     48-60     60-72     72-84    84-96    96-108   108-120   120-132
(All)  1.582216  1.301914  1.142205  1.071625  1.059935  1.022835  1.00511  0.997636  0.992918  0.999179

We can also use multiple drop parameters together. Let’s say, we want to drop all link ratio(s) above 1.25 and below 1.0, but only drop these link ratios when there are 3 or more link ratios remaining.

tri = cl.load_sample("xyz")
print(
    cl.Development(drop_above=1.25, drop_below=1.0, preserve=3)
    .fit_transform(tri["Incurred"])
    .link_ratio
)

         12-24     24-36     36-48     48-60     60-72     72-84     84-96    96-108   108-120   120-132
1998       NaN       NaN  1.108227  1.067528  1.064392  1.044146  1.114243  0.987596  0.979707  0.999179
1999       NaN  1.237646  1.197135  1.144305  1.057447  1.055967       NaN  1.011131  1.001436       NaN
2000  1.196032  1.168062  1.239452  1.086354  1.168543  1.072291  1.015048  0.993094       NaN       NaN
2001  1.353175       NaN       NaN       NaN  1.085689  1.037834  1.006668       NaN       NaN       NaN
2002  1.590040       NaN       NaN  1.179122  1.096524       NaN       NaN       NaN       NaN       NaN
2003  1.760957       NaN       NaN  1.089595  1.003210       NaN       NaN       NaN       NaN       NaN
2004  2.364225       NaN  1.218140       NaN       NaN       NaN       NaN       NaN       NaN       NaN
2005  1.654181       NaN  1.004478       NaN       NaN       NaN       NaN       NaN       NaN       NaN
2006  1.728479  1.043199       NaN       NaN       NaN       NaN       NaN       NaN       NaN       NaN
2007  1.629204       NaN       NaN       NaN       NaN       NaN       NaN       NaN       NaN       NaN

Notice that the link ratios above 1.25 and below 1.0 are not dropped, unless there are 3 or more link ratios remaining. For example, the 12-24 link ratio is not dropped because there are 2 valid non-NaN link ratios remaining after removing all link ratios above 1.25 and below 1.0. While the 24-36 link ratio is dropped because there are still 3 valid non-NaN link ratios remaining after removing all link ratios above 1.25 and below 1.0.

Let’s inspect the LDFs.

ldf = (
    cl.Development(drop_above=1.25, drop_below=1.0, preserve=3)
    .fit(tri["Incurred"])
    .ldf_
)
print(ldf)

          12-24     24-36     36-48     48-60     60-72     72-84     84-96    96-108   108-120   120-132
(All)  1.675693  1.105627  1.127842  1.119324  1.076968  1.053434  1.027623  0.997636  0.992918  0.999179

Using other average methods, we can see that the loss development factors are different.

tri = cl.load_sample("xyz")
ldf = (
    cl.Development(average="simple").fit(tri["Incurred"]).ldf_
)
print(ldf)

          12-24    24-36    36-48     48-60     60-72     72-84     84-96    96-108   108-120   120-132
(All)  1.659537  1.35064  1.22277  1.119155  1.079301  1.039863  1.031011  0.997274  0.990571  0.999179
fit(X: TriangleLike, y: None = None, sample_weight: None = None)[source]#

Fit the model with X.

Parameters:
XTriangleLike

Set of LDFs to which the Munich adjustment will be applied.

yNone

Ignored

sample_weightNone

Ignored

Returns:
selfobject

Returns the instance itself.

transform(X)[source]#

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

Parameters:
XTriangle

The triangle to be transformed

Returns:
X_newNew triangle with transformed attributes.

Inherited Methods

Development.fit_transform

Fit to data, then transform it.

Development.get_metadata_routing

Get metadata routing of this object.

Development.get_params

Get parameters for this estimator.

Development.pipe

Development.set_backend

Converts triangle array_backend.

Development.set_output

Set output container.

Development.set_params

Set the parameters of this estimator.

Development.to_json

Serializes triangle object to json format

Development.to_pickle

Serializes triangle object to pickle.