A Multi-Task Network Approach for Calculating Discrimination-Free Insurance Prices

Abstract

In applications of predictive modeling, such as insurance pricing, indirect or proxy discrimination is an issue of major concern. Namely, there exists the possibility that protected policyholder characteristics are implicitly inferred from non-protected ones by predictive models, and are thus having an undesirable (and possibly illegal) impact on prices. A technical solution to this problem relies on building a best-estimate model using all policyholder characteristics (including protected ones) and then averaging out the protected characteristics for calculating individual prices. However, such approaches require full knowledge of policyholders' protected characteristics, which may in itself be problematic. Here, we address this issue by using a multi-task neural network architecture for claim predictions, which can be trained using only partial information on protected characteristics, and it produces prices that are free from proxy discrimination. We demonstrate the proposed method on both synthetic data and a real-world motor claims dataset, in which proxy discrimination can be observed. In both cases we find that the predictive accuracy of the multi-task network is comparable to a conventional feed-forward neural network, when full information is available. Moreover, the multi-task network has clearly superior performance in the case of partially missing policyholder information.

Keywords: indirect discrimination, proxy discrimination, discrimination-free insurance pricing, unawareness price, best-estimate price, protected information, discriminatory covariates, fairness, incomplete information, multi-task learning, multioutput network

JEL Classification: G22, C45, C10, C13, C20