Antidiscrimination Insurance Pricing: Regulations, Fairness Criteria, and Models

Figures & data

TABLE 1 Comparison between Different Regulations

Regulation	Fairness criteria	Representative model
No regulation	Neither	M0
Restriction on a protected variable	Neither	M0*
Prohibition on a protected variable	Individual	MU or MC
Restriction on a proxy variable	Individual	MU*
Prohibition on a proxy variable	Individual	MU*
Disparate impact standard	Group	MDP or MCDP
Community rating	Group	MDP or MCDP
Affirmative action	Neither	None

Note: M0, MU, MC, MDP, and MCDP are acronyms for the five models introduced in Section 4. M0 denotes the full model, MU denotes the unawareness model that is fit using only non-protected variables, MDP denotes the model satisfying demographic parity by fitting with unbiased data, MCDP denotes the model satisfying conditional demographic parity by fitting with legitimate and debiased nonlegitimate variables, and MC denotes the model satisfying Definition 4 (Controlling for the Protected Variable) in Section 3. For representative models, M0 denotes the original M0 discussed in Sections 4 and 5, and M0* denotes M0 or M0 with some adjustments; for example, if insurers are restricted from charging extremely high premiums for policyholders from a high-risk category that exceeds a certain threshold compared to the reference category, we may need to adjust the model coefficients for the high-risk category to meet regulatory requirements. As a further extension of MU, the proxies of a protected variable are also prohibited from being used and therefore are removed from modeling.

TABLE 2 The Linkage between Fair Pricing Models and Fairness Criteria

Model	Definition
M0	—
MU	FTU
MDP	DP
MCDP	CDP
MC	CPV

Figure 1. Probability Density Plots of Age by Gender Before and after Adjusting for Age Using the DI Remover.

Figure 2. The Effect of DI Remover by Age and Gender.

TABLE 3 Comparison of Means of Predicted Pure Premiums by Model, Method, and Gender after Portfolio-Level Adjustment

	M0	MU	MU’	MDP	MDP’	MCDP	MCDP’	MC
GLM male	130.47	114.03	118.53	117.38	120.78	115.26	119.40	113.95
GLM female	95.66	124.05	116.25	118.23	112.34	121.90	114.73	124.18
XGBoost male	131.06	114.41	118.45	117.74	120.63	116.59	119.97	114.24
XGB female	94.50	123.39	116.37	117.61	112.60	119.61	113.74	123.68

Figure 3. Fairness–Accuracy Plot (Scenario 1).

Figure 4. Fairness–Accuracy Plot (Scenario 2).

Figure 5. Fairness–Accuracy Plot (Scenario 3).

Figure 6. Fairness–Accuracy Plot (Scenario 4).

Figure 7. Double Lift Charts by Gender (GLM MDP versus GLM MU).

Figure 8. Double Lift Chart (GLM MDP versus GLM MU).

Figure 9. Relative and Average Premium Difference (GLM Models versus GLM MU).

Figure 10. Relative and Average Premium Difference (GLM Models versus GLM M0).

Figure C.1. Double Lift Charts by Gender (GLM MCDP versus GLM MU).

Figure C.2. Double Lift Chart (GLM MCDP versus GLM MU).

Figure C.3. Double Lift Charts by Gender (XGBoost MDP versus GLM MU).

Figure C.4. Double Lift Chart (XGBoost MDP versus GLM MU).

Figure C.5. Double Lift Charts by Gender (XGBoost MCDP versus GLM MU).

Figure C.6. Double Lift Chart (XGBoost MCDP versus GLM MU).

Figure C.7. Relative and Average Premium Difference (XGBoost Models versus GLM MU).

Figure C.8. Relative and Average Premium Difference (XGBoost Models versus GLM M0).

Figure C.9. Relative and Average Premium Difference (GLM Models vs. Actual Claim Costs).

Figure C.10. Relative and Average Premium Difference (XGBoost Models versus Actual Claim Costs).