actuarcredibility 0.1.1

Credibility models for actuarial pricing: Bühlmann, Bühlmann-Straub, Jewell, Hachemeister, and Bayesian extensions.

actuarcredibility

Python library for actuarial credibility models. Covers Bühlmann, Bühlmann-Straub, Jewell hierarchical, Hachemeister regression, classical limited-fluctuation, and an optional Bayesian model via PyMC. Outputs integrate with pandas DataFrames. References Bühlmann & Gisler (2005) and Klugman ch. 20.

Installation

From PyPI:

pip install actuarcredibility

From source:

git clone https://github.com/CosmikArt/actuarcredibility.git
cd actuarcredibility
pip install -e .

With Bayesian extensions:

pip install actuarcredibility[bayesian]

Quickstart

Buhlmann-Straub on multi-year loss data:

import pandas as pd
from actuarcredibility import BuhlmannStraubModel

# Multi-year loss experience by risk class
data = pd.DataFrame({
    "risk_class": ["A", "A", "A", "B", "B", "B", "C", "C", "C"],
    "year": [2021, 2022, 2023, 2021, 2022, 2023, 2021, 2022, 2023],
    "loss_ratio": [0.62, 0.58, 0.65, 0.81, 0.77, 0.84, 0.45, 0.52, 0.48],
    "earned_premium": [5_000_000, 5_200_000, 5_500_000,
                       2_000_000, 2_100_000, 2_300_000,
                       8_000_000, 8_500_000, 9_000_000],
})

model = BuhlmannStraubModel()
model.fit(
    data,
    group_col="risk_class",
    observation_col="loss_ratio",
    weight_col="earned_premium",
)

# Credibility factor per risk class
print(model.credibility_factor())

# Credibility-weighted premium estimate
print(model.credibility_premium())

Features

Module	Description
buhlmann	BuhlmannModel, BuhlmannStraubModel. Non-parametric credibility with Bühlmann-Gisler unbiased structural estimators.
hierarchical	JewellHierarchical: multi-level hierarchical credibility for nested portfolios (region → territory → risk_class, etc.).
regression	HachemeisterRegression (regression credibility with covariates or a time trend; weighted least squares per group).
classical	LimitedFluctuationCredibility. Square-root rule for partial credibility, configurable tolerance and probability.
bayesian	BayesianCredibility is a PyMC hierarchical normal model with posterior credibility factors. Optional dependency.
diagnostics	variance_decomposition, credibility_curve, shrinkage_summary, compare_models

More examples

Classical limited fluctuation

from actuarcredibility import LimitedFluctuationCredibility

cred = LimitedFluctuationCredibility(k=0.05, p=0.90)
cred.full_credibility_standard()           # 1082 claims
cred.credibility_factor(n_claims=500)      # ~0.6797
cred.credibility_premium(observed=0.72, prior=0.65, n_claims=500)

Hachemeister trend credibility

import pandas as pd
from actuarcredibility import HachemeisterRegression

data = pd.DataFrame({
    "state": ["CA", "CA", "CA", "TX", "TX", "TX"],
    "year": [2021, 2022, 2023, 2021, 2022, 2023],
    "avg_claim_cost": [4500, 4700, 4900, 5200, 5400, 5600],
    "claim_count": [120, 130, 140, 80, 85, 95],
})

model = HachemeisterRegression().fit(
    data,
    group_col="state",
    observation_col="avg_claim_cost",
    time_col="year",
    weight_col="claim_count",
)
model.coefficients()              # credibility-weighted (intercept, slope) per state
model.predict("CA", year=2026)    # forecast next-year average cost

Hierarchical (Jewell)

import pandas as pd
from actuarcredibility import JewellHierarchical

data = pd.DataFrame({
    "region": (["W"]*8 + ["E"]*8),
    "territory": (["W1","W1","W2","W2"]*2 + ["E1","E1","E2","E2"]*2),
    "risk_class": (["A","B"]*8),
    "year": [2022, 2022, 2022, 2022, 2023, 2023, 2023, 2023] * 2,
    "loss_ratio": [0.62, 0.71, 0.58, 0.69, 0.65, 0.74, 0.60, 0.71,
                   0.81, 0.75, 0.66, 0.72, 0.83, 0.77, 0.68, 0.74],
    "earned_premium": [2_000_000]*16,
})

model = JewellHierarchical().fit(
    data,
    hierarchy_cols=["region", "territory", "risk_class"],
    observation_col="loss_ratio",
    weight_col="earned_premium",
)
model.credibility_factor(level="territory")
model.credibility_premium()       # finest-level credibility premium

Diagnostics

import pandas as pd
from actuarcredibility import BuhlmannStraubModel
from actuarcredibility.diagnostics import (
    variance_decomposition, credibility_curve, shrinkage_summary,
)

data = pd.DataFrame({
    "risk": ["A","A","A","B","B","B","C","C","C"],
    "year": [2021,2022,2023]*3,
    "loss_ratio": [0.62,0.58,0.65,0.81,0.77,0.84,0.45,0.52,0.48],
    "earned_premium": [5_000_000,5_200_000,5_500_000,
                       2_000_000,2_100_000,2_300_000,
                       8_000_000,8_500_000,9_000_000],
})

model = BuhlmannStraubModel().fit(data, "risk", "loss_ratio", "earned_premium")
variance_decomposition(model)     # v, a, between-share, k = v/a
credibility_curve(model)          # Z(w) tabulated for plotting
shrinkage_summary(model)          # raw vs. credibility distance to grand mean

References

• Buhlmann, H. (1967). "Experience Rating and Credibility." ASTIN Bulletin, 4(3), 199-207.
• Buhlmann, H. & Gisler, A. (2005). A Course in Credibility Theory and its Applications. Springer.
• Klugman, S.A., Panjer, H.H. & Willmot, G.E. Loss Models: From Data to Decisions. Wiley.
• Jewell, W.S. (1975). "The Use of Collateral Data in Credibility Theory: A Hierarchical Model." Giornale dell'Istituto Italiano degli Attuari, 38, 1-16.
• Hachemeister, C.A. (1975). "Credibility for Regression Models with Application to Trend." In Credibility: Theory and Applications, P.M. Kahn (ed.), Academic Press.
• Casualty Actuarial Society. Exam 5 Study Notes: Credibility.

Contributing

Run pytest before sending a PR.

Author

Isaac López

MIT License. See LICENSE.