Tag Archives: mitigation

Publications

Measuring and mitigating biases in motor insurance pricing

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Our paper, with Mulah Moriah and Franck Vermet, Measuring and mitigating biases in motor insurance pricing, has been recenlty published in the European Actuarial Journal,

The non-life insurance sector operates within a highly competitive and tightly regulated framework, confronting a pivotal juncture in the formulation of pricing strategies. Insurers are compelled to harness a range of statistical methodologies and available data to construct optimal pricing structures that align with the overarching corporate strategy while accommodating the dynamics of market competition. Given the fundamental societal role played by insurance, premium rates are subject to rigorous scrutiny by regulatory authorities. Consequently, the act of pricing transcends mere statistical calculations and carries the weight of strategic and societal factors. These multifaceted concerns may drive insurers to establish equitable premiums, considering various variables. For instance, regulations mandate the provision of equitable premiums, considering factors such as policyholder gender. Or mutualist groups in accordance with respective corporate strategies can implement age-based premium fairness. In certain insurance domains, the presence of serious illnesses or disabilities are emerging as new dimensions for evaluating fairness. Regardless of the motivating factor prompting an insurer to adopt fairer pricing strategies for a specific variable, the insurer must possess the capability to define, measure, and ultimately mitigate any fairness biases inherent in its pricing practices while upholding standards of consistency and performance. This study seeks to provide a comprehensive set of tools for these endeavors and assess their effectiveness through practical application in the context of automobile insurance. Results show that fairness bias can be found in historical data and models, and that fairer outcomes can be obtained by more fairness-aware approaches.

Seminar

Online Seminar Finance & Modeling, Centre d’Économie de la Sorbonne

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In a week,  I will give a talk at the Modélisation Financière seminar (“Online Seminar Finance & Modeling” according to the invitation) on Using optimal transport to mitigate unfair predictions. Slides are now on line.

The insurance industry is heavily reliant on predictions of risks based on characteristics of potential customers. Although the use of said models is common, researchers have long pointed out that such practices perpetuate discrimination based on sensitive features such as gender or race. Given that such discrimination can often be attributed to historical data biases, an elimination or at least mitigation is desirable. With the shift from more traditional models to machine-learning based predictions, calls for greater mitigation have grown anew, as simply excluding sensitive variables in the pricing process can be shown to be ineffective. In this talk, we first investigate why predictions are a necessity within the industry and why correcting biases is not as straightforward as simply identifying a sensitive variable. We then propose to ease the biases through the use of Wasserstein barycenters instead of simple scaling. To demonstrate the effects and effectiveness of the approach we employ it on real data and discuss its implications. The talk will be based on recent work with François Hu and Philipp Ratz (2310.20508, 2309.06627, 2306.12912 and 2306.10155).

MAT998P

Fairness and discrimination, PhD Course, #9 Mitigation, Pre-processing and In-processing

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Finally, after defining (and quantifying) “group fairness“ and “individual fairness“, we can now start to discuss the idea of mitigating a possible discrimination. Here, we will see, how based on some data that were initially collected, and a model (a pricing model), it is possible to remove the discrimination in our pricing model.

Biases everywhere

As mentioned previously, insurance princing is based on the use of different datasets, at least one from “claims” and one from “underwriting”. And obviously, there might be biases in those data, conscious, or intended, or not.

Somehow, idea of tackling the problem from the end, as proposed, may not be the right one, and it might be better to tackle it from the beginning, through the biases in the data. The outcome of models will be less discriminatory if we could get rid of sexist or racist bias in underwriting, or even in the assessment of claims costs. Unfortunately, I cannot discuss that here since I do not have data that could be used to assess selection biases related to sensitive attributes.

On mitigation…

From a philosophical perspective, asking for mitigation might lead to some paradoxes.  I mention here two statements, by two judges in the U.S., that have very opposite perspective on the same problem,

versus

I will not talk much about those philosophical aspects (discussed a bit more in the textbook), we will not discuss how we can achieve fairness if required.

Interestingly, we have a nice property, on the price to pay to achieve fairness (price in terms of risk)

More precisely, we have the following result,

Interestingly, we have not only a lower bound, we can actually reach that bound (we will discuss that point next week).

Pre-processing

The first approach is related to the idea of “distorting” inputs, to get legitimate explanatory variables that are uncorrelated with sensitive ones.

If that makes sense in the context of linear models, it is not working well in the general case.

But one should not be (too) suprised: as mentioned in a previous post, on independence (and correlation), there is no statistical guarantees to keep it with nonlinear transforms of variables

or

It is what we observe on our datasets.

In-processing

An alternative is to use a penalized approach, where fairness is added as the constraint in the optimization procedure. For example Zafar et al. (2017), considered the following approach, with a constraint based on the covariance between the outcome and the sensitive attribute. We can adapt it for non-linear models.

We can look at the evolution of \widehat{\boldsybol{\beta}} as a function of c.

We can also visualize the evolution of predictions,

(including prediction for unwaware model, blind to the sensitive attribute)

On this slide, we can see that we have a tradeoff between accuracy and fairness.

It is also possible to visualize the distance between the distributions of scores in the two groups. We can see that c\to0 gives here strong fairness actuarlly, since Wasserstein distance tends to 0.

An alternative that we can find in the litterature (that I include in the in-processing section) is based on adversarial learning,

Formally, it is

which is related to minimax theorems

Standard references about adversarial learning and fairness are the following

Next week, we will discuss post-processing approaches.