Tail model configurations

GeneralizedBondy

class ledger_analytics.GeneralizedBondy(id: str, name: str, model_type: str, config: dict[str, Any] | None, model_class: str, endpoint: str, requester: Requester, asynchronous: bool = False)

GeneralizedBondy.

This model implements, by default, a Bayesian version of the Generalized Bondy tail development model, with the form:

\[\begin{split}\mathrm{LR}_{ij} &\sim \mathrm{Gamma(\mu_{ij}, \sigma_{ij}^2)}\\ \mu_{ij} &= ATA_{j} y_{ij - 1}\\ ATA_{j} &= \exp( ATA_{\text{init}} \beta^{j} )\\ \sigma_{ij}^2 &= \exp(\sigma_{\text{int}} + \sigma_{\text{slope}} j - \log(\mathrm{EP}_{i})), \quad{\forall j \in [1, M]}\end{split}\]

See the model-specific documentation in the User Guide for more details.

The fit and predict configurations are controlled by Config and PredictConfig classes, respectively.

class Config(*, loss_family: ~typing.Annotated[~typing.Literal['Gamma', 'Lognormal', 'Normal', 'InverseGaussian'], ~pydantic.functional_validators.BeforeValidator(func=~ledger_analytics.config.<lambda>, json_schema_input_type=PydanticUndefined)] = 'Gamma', loss_definition: ~typing.Literal['paid', 'reported', 'incurred'] = 'paid', recency_decay: str | float | None = None, line_of_business: str | None = None, min_rel_pred: float = 0.0, dev_lag_intercept: float = 0.0, priors: dict[str, list[float] | float] | None = None, informed_priors_version: str | None = None, autofit_override: dict[str, float | int | None] = None, prior_only: bool = False, seed: int | None = None)

GeneralizedBondy model configuration class.

loss_family

the likelihood family to use. One of "Gamma", "Lognormal", "Normal" or "InverseGaussian". Defaults to "Gamma". See the LossFamily type hint class in ledger_analytics.config.

Type:

Literal[‘Gamma’, ‘Lognormal’, ‘Normal’, ‘InverseGaussian’]

loss_definition

the field to model in the triangle. One of "paid" "reported" or "incurred".

Type:

Literal[‘paid’, ‘reported’, ‘incurred’]

recency_decay

geometric decay parameter to downweight earlier diagonals (see Modeling rationale… section in the User Guide). Defaults to 1.0 for no geometric decay. Can be "lookup" to choose based on line_of_business.

Type:

str | float | None

line_of_business

Line of business used to specify informed priors. Must be provided if informed_priors_version is not None.

Type:

str | None

min_rel_pred

Minimum relative prediction for the one-step ahead predictions. This is a multiplier of the previous period’s loss. Setting to 1.0 indicates that future losses should be strictly at least the prior period’s loss amount, avoiding negative development patterns.

Type:

float

dev_lag_intercept

the development lag offset to apply in the exponential of the Bondy exponent term. By default, this is 0.0, but can be set to a suitable development lag (in months) to center the Bondy parameters.

Type:

float

priors

dictionary of priors. Defaults to None to use the default priors. See the DefaultPriors class for default (non line-of-business) priors.

Type:

dict[str, list[float] | float] | None

informed_priors_version

If line_of_business is set, the priors are based on Ledger Investing’s proprietary values derived from industry data. "latest" uses priors derived from the most recent industry data. Defaults to None.

Type:

str | None

autofit_override

override the MCMC autofitting procedure arguments. See the documentation for a fully description of options in the User Guide.

Type:

dict[str, float | int | None]

prior_only

should a prior predictive simulation be run?

Type:

bool

seed

Seed to use for model sampling. Defaults to None, but it is highly recommended to set.

Type:

int | None

class DefaultPriors(value)

Default priors for GeneralizedBondy.

Attributes:

class PredictConfig(*, max_dev_lag: float | None = None, max_eval: date | None = None, eval_resolution: tuple[int, str] | None = None, include_process_risk: bool = True)

Sherman

class ledger_analytics.Sherman(id: str, name: str, model_type: str, config: dict[str, Any] | None, model_class: str, endpoint: str, requester: Requester, asynchronous: bool = False)

Sherman.

This model implements, by default, a Bayesian version of Sherman (1984)’s inverse power curve tail development model,

• Sherman, RE (1984). Extrapolating, smoothing and interpolating

  development factors. PCAS 71, p. 122-155.

It has the form:

\[\begin{split}\mathrm{LR}_{ij} &\sim \mathrm{Gamma(\mu_{ij}, \sigma_{ij}^2)}\\ \mu_{ij} &= ATA_{ij} y_{ij - 1}\\ ATA_{j} &= 1 + \exp( ATA_{\text{int}} - \beta \log(j) )\\ \sigma_{ij}^2 &= \exp(\sigma_{\text{int}} + \sigma_{\text{slope}} j - \log(\mathrm{EP}_{i})), \quad{\forall j \in [1, M]}\end{split}\]

See the model-specific documentation in the User Guide for more details.

The fit and predict configurations are controlled by Config and PredictConfig classes, respectively.

class Config(*, loss_family: ~typing.Annotated[~typing.Literal['Gamma', 'Lognormal', 'Normal', 'InverseGaussian'], ~pydantic.functional_validators.BeforeValidator(func=~ledger_analytics.config.<lambda>, json_schema_input_type=PydanticUndefined)] = 'Gamma', loss_definition: ~typing.Literal['paid', 'reported', 'incurred'] = 'paid', recency_decay: str | float | None = None, line_of_business: str | None = None, min_rel_pred: float = 0.0, dev_lag_intercept: float = 0.0, priors: dict[str, list[float] | float] | None = None, autofit_override: dict[str, float | int | None] = None, prior_only: bool = False, seed: int | None = None)

Sherman model configuration class.

loss_family

the likelihood family to use. One of "Gamma", "Lognormal", "Normal" or "InverseGaussian". Defaults to "Gamma". See the LossFamily type hint class in ledger_analytics.config.

Type:

Literal[‘Gamma’, ‘Lognormal’, ‘Normal’, ‘InverseGaussian’]

loss_definition

the field to model in the triangle. One of "paid" "reported" or "incurred".

Type:

Literal[‘paid’, ‘reported’, ‘incurred’]

recency_decay

geometric decay parameter to downweight earlier diagonals (see Modeling rationale… section in the User Guide). Defaults to 1.0 for no geometric decay. Can be "lookup" to choose based on line_of_business.

Type:

str | float | None

min_rel_pred

Minimum relative prediction for the one-step ahead predictions. This is a multiplier of the previous period’s loss. Setting to 1.0 indicates that future losses should be strictly at least the prior period’s loss amount, avoiding negative development patterns.

Type:

float

dev_lag_intercept

the development lag offset to apply in the exponential of the Bondy exponent term. By default, this is 0.0, but can be set to a suitable development lag (in months) to center the Bondy parameters.

Type:

float

priors

dictionary of priors. Defaults to None to use the default priors. See the DefaultPriors class for default (non line-of-business) priors.

Type:

dict[str, list[float] | float] | None

autofit_override

override the MCMC autofitting procedure arguments. See the documentation for a fully description of options in the User Guide.

Type:

dict[str, float | int | None]

prior_only

should a prior predictive simulation be run?

Type:

bool

seed

Seed to use for model sampling. Defaults to None, but it is highly recommended to set.

Type:

int | None

class DefaultPriors(value)

Default priors for Sherman.

Attributes:

class PredictConfig(*, max_dev_lag: float | None = None, max_eval: date | None = None, eval_resolution: tuple[int, str] | None = None, include_process_risk: bool = True)

ClassicalPowerTransformTail

class ledger_analytics.ClassicalPowerTransformTail(id: str, name: str, model_type: str, config: dict[str, Any] | None, model_class: str, endpoint: str, requester: Requester, asynchronous: bool = False)

ClassicalPowerTransformTail model.

This model implements a generalization of classical power transform tail models on age-to-age factors (ATAs) which, by default, fits a model with maximum likelihood estimation of the form:

\[\begin{split}\log ATA_{j} &\sim \mathrm{Normal(\mu_{j}, \sigma^2)}\\ \mu_{j} &= \beta_{\text{int}} + \beta_{j} \text{L}_j\\ \beta_{j} &= \lambda - 1 - \beta_{\text{slope}}\\ \text{L}_j &= j^{\lambda-1} / \lambda\end{split}\]

where \(\log ATA\) represents log-scale ATAs, and \(\lambda`\) is a Box-Cox transformation parameter. The latter can be set to switch between exponential decay, Sherman and Clark square-root tail models. See the model-specific documentation in the User Guide for more details.

The fit and predict configurations are controlled by Config and PredictConfig classes, respectively.

class Config(*, loss_definition: Literal['paid', 'reported', 'incurred'] = 'paid', lambda_: float = 1.0, recency_decay: str | float | None = None, min_rel_pred: float = 0.0, priors: dict[str, list[float] | float] | None = None, prior_only: bool = False, seed: int | None = None)

ClassicalPowerTransformTail model configuration class.

loss_definition

the field to model in the triangle. One of "paid" "reported" or "incurred".

Type:

Literal[‘paid’, ‘reported’, ‘incurred’]

lambda_

Box-Cox transformation parameter applied to development lag (as measured in years). lambda_=1.0 is equivalent to the exponential decay tail model. lambda_=0.0 is equivalent to the Sherman inverse-power tail model. lambda_=0.5 is equivalent to the Clark square-root tail model.

Type:

float

recency_decay

geometric decay parameter to downweight earlier diagonals (see Modeling rationale… section in the User Guide). Defaults to 1.0 for no geometric decay. Can be "lookup" to choose based on line_of_business.

Type:

str | float | None

min_rel_pred

Minimum relative prediction for the one-step ahead predictions. This is a multiplier of the previous period’s loss. Setting to 1.0 indicates that future losses should be strictly at least the prior period’s loss amount, avoiding negative development patterns.

Type:

float

priors

dictionary of priors. Defaults to None to use the default priors. See the DefaultPriors class for default (non line-of-business) priors.

Type:

dict[str, list[float] | float] | None

prior_only

should a prior predictive simulation be run?

Type:

bool

seed

Seed to use for model sampling. Defaults to None, but it is highly recommended to set.

Type:

int | None

class DefaultPriors(value)

Default priors for ClassicalPowerTransformTail.

Attributes:

class PredictConfig(*, max_dev_lag: float | None = None, max_eval: date | None = None, eval_resolution: tuple[int, str] | None = None, include_process_risk: bool = True)