A Discrimination-Free Premium under a Causal Framework

Abstract

We examine the discrimination-free premium in Lindholm et al. within a theoretical causal inference framework, and we consider its societal context to assess when the pricing formula should be used. We consider the insurance pricing problem through the use of directed acyclic graphs. This particular tool allows us to rigorously define an insurance risk factor in a causal framework. We then use this definition in assessing the appropriate application of the discrimination-free premium through three simplified pricing examples, including a health insurance policy and two personal automobile insurance policies with different coverages. From our findings, we suggest criteria for the application of the discrimination-free premium that is dependent on the risk factors and the social context.

ACKNOWLEDGMENTS

We thank the anonymous reviewers and editor for their constructive comments, which allowed us to significantly improve the article.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Formally, to read dependencies in distribution from the DAG, we also need the minimality condition to hold, which says that the probability distribution does not satisfy any additional independencies to those imposed by the associated DAG (Neal 2020).

2 Frees and Huang (2023) pointed out that policyholders are more likely to accept the use of rating factors that are understood to have a causal association with the loss.

3 A Markovian model coupled with a stable distribution with respect to a DAG entails the minimality condition. See Peters, Janzing, and Schölkopf (2017) for a proof.

Additional information

Funding

We gratefully acknowledge financial support from the Natural Sciences and Engineering Research Council of Canada (NSERC), under Grant No. RGPIN-2018-03754 to MH and Grant No. RGPIN-2020-04015 to PM.