Discrimination-insensitive pricing

2026-03-17

AI Summary

This study addresses the challenge of achieving fair pricing in finance, credit, and insurance without directly using protected attributes such as gender or race. The authors propose a discrimination-insensitive pricing framework that constructs a “pricing” probability measure completely invariant to protected covariates, while minimizing its Kullback–Leibler (KL) divergence from the real-world measure under fairness constraints. They introduce a constrained KL barycenter model and rigorously establish the existence and uniqueness of its solution in the presence of multiple protected variables. By integrating measure-theoretic and convex optimization techniques, the framework is made computationally tractable. Numerical experiments demonstrate that the method effectively generates fair premiums and outperforms existing benchmarks in actuarial literature, confirming both its theoretical soundness and practical efficacy.

Technology Category

• Game Theory and Economic Paradigms: Fair Division
• Machine Learning: Privacy
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Security and Privacy: Large-scale security measurements

Abstract

Rendering fair prices for financial, credit, and insurance products is of ethical and regulatory interest. In many jurisdictions, discriminatory covariates, such as gender and ethnicity, are prohibited from use in pricing such instruments. In this work, we propose a discrimination-insensitive pricing framework, where we require the pricing principle to be insensitive to the (exogenously determined) protected covariates, that is the sensitivity of the pricing principle to the protected covariate is zero. We formulate and solve the optimisation problem that finds the nearest (in Kullback-Leibler (KL) divergence) "pricing" measure to the real world probability, such that under this pricing measure the principle is discrimination-insensitive. We call the solution the discrimination-insensitive measure and provide conditions for its existence and uniqueness. In situations when there are more than one protected covariates, the discrimination-insensitive pricing measure might not exist, and we propose a two-step procedure. First, for each protected covariate separately, we find the measure under which the pricing principle becomes insensitivity to that covariate. Second we reconcile these measures through a constrained barycentre model. We provide a close-form solution to this problem and give conditions for existence and uniqueness of the constrained barycentre pricing measure. As an intermediary result, we prove the representation, existence, and uniqueness of the KL barycentre of general probability measures, which may be of independent interest. Finally, in a numerical illustration, we compare our discrimination-insensitive premia and the constrained barycentre pricing measure with recently proposed fair premia from the actuarial literature.

Problem

• discrimination-insensitive pricing
• fair pricing
• protected covariates
• KL divergence
• pricing fairness

Innovation

• discrimination-insensitive pricing
• Kullback-Leibler divergence
• fair pricing
• constrained barycentre
• protected covariates