A Fair Pricing Model via Adversarial Learning

We recently uploaded a revised version of our joint paper A Fair Pricing Model via Adversarial Learning, on ArXiv.

At the core of insurance business lies classification between risky and non-risky insureds, actuarial fairness meaning that risky insureds should contribute more and pay a higher premium than non-risky or less-risky ones. Actuaries, therefore, use econometric or machine learning techniques to classify, but the distinction between a fair actuarial classification and `discrimination’ is subtle. For this reason, there is a growing interest about fairness and discrimination in the actuarial community Lindholm et al. (2022). Presumably, non-sensitive characteristics can serve as substitutes or proxies for protected attributes. For example, the color and model of a car, combined with the driver’s occupation, may lead to an undesirable gender bias in the prediction of car insurance prices. Fairness in insurance pricing is a relatively new and much-requested topic, especially in light of new laws and regulations and past issues encountered in practice (Embrechts and Wüthrich, 2022; Frees and Huang, 2021; Gao and Wüthrich, 2018). Consequently, companies/regulators are looking for new methodologies to ensure a sufficient level of fairness while maintaining an adequate accuracy of predictive models. This paper discusses the importance of adapting the traditional fairness algorithms to specific real-life applications and, in particular, to insurance pricing. We claim that mitigating undesired biases with a generic fair algorithm can be counterproductive insurance. We will show that traditional Fair-ML as adversarial methods are not currently adequate for insurance pricing. Therefore, for these purposes, we have developed a more suitable and effective framework to satisfy a fairness objective while maintaining a sufficient level of predictor accuracy. Inspired by the recent approaches, Blier et al. (2021) and Wuthrich et al. (2021), that have shown the value of autoencoders in pricing, we will show that (2) it can be generalized to multiple pricing factors (geographic, car type), (3) it is more adapted for a fairness context (since it allows to debias the set of pricing components): We extend this main idea to a general framework in which a single whole pricing model is trained by generating the geographic and car pricing components needed to predict the pure premium while mitigating the unwanted bias according to the desired metric. 

There are more examples in this revised version, including the case of a non-binary target, and a non-binary senssitive attribute, such as a spatial one

Qu’est-ce que l’assurance ?

Avec un peu de retard, je profite de ce moment de relâche pour mentionner une entrevue, parue chez Dalloz Actualités,  avec Rodolphe Bigot et Amandine Cayol.

Quel est l’intérêt d’aborder les mécanismes de l’assurance de manière multidisciplinaire en 2022 ?

Depuis une dizaine d’années, on a l’impression que l’univers des risques est en forte expansion dans nos sociétés, et qu’il croît avec le niveau de développement. Jusqu’à récemment, il y avait une attitude générale de désintérêt à l’égard des principes et des techniques de couverture des risques ou de transfert de ces risques, que ce soit à des tiers, à des assureurs, à des réassureurs, aux marchés financiers ou encore à la puissance publique. La demande sociale de protection augmente avec l’accumulation de richesses, l’information des citoyens, et la dangerosité réelle ou ressentie des technologies. Par ailleurs, le débat sur le rôle de l’État et l’implication des finances publiques dans la protection des citoyens est désormais largement ouvert. Les techniques et les modalités de gestion de l’assurance sont donc des éléments importants de l’analyse du fonctionnement de la société. Malgré cet intérêt collectif, force est de constater que les techniques de la gestion des risques sont souvent méconnues par le grand public, y compris chez bon nombre d’étudiants, auxquels les fondamentaux sont généralement exposés sporadiquement, dans des formations spécialisées trop tôt (droit, économie, mathématiques et science en général) alors même que l’assurance offre des perspectives importantes de développement de l’emploi. Ainsi, l’assurance nécessite par nature une approche multidisciplinaire : mathématiques et actuariat, économie, mais aussi droit et sciences de l’ingénieur. à suivre

Quantifying fairness and discrimination in predictive models 

In about ten days, late in the evening (Montréal time), I will attend the 16th Annual Conference of Thailand Econometric Society (on Machine Learning for Econometrics and Related Topics), at Chiang Mai University (มหาวิทยาลัยเชียงใหม่). I will give a talk (introductionary talk, at 21:30 pm, with the jet lag) on quantifying fairness and discrimination in predictive models (the state-of-the-art paper I will present is online on arXiv) and the slides are now also available (I won’t be able to go to Chiang Mai, unfortunately, and I will be on zoom).

The analysis of discrimination has long interested economists and lawyers. In recent years, the literature in computer science and machine learning has become interested in the subject, offering an interesting re-reading of the topic. These questions are the consequences of numerous criticisms of algorithms used to translate texts or to identify people in images. With the arrival of massive data, and the use of increasingly opaque algorithms, it is not surprising to have discriminatory algorithms, because it has become easy to have a proxy of a sensitive variable, by enriching the data indefinitely. According to Kranzberg (1986), “technology is neither good nor bad, nor is it neutral”, and therefore, “machine learning won’t give you anything like gender neutrality `for free’ that you didn’t explicitely ask for”, as claimed by Kearns et a. (2019). In this article, we will come back to the general context, for predictive models in classification. We will present the main concepts of fairness, called group fairness, based on independence between the sensitive variable and the prediction, possibly conditioned on this or that information. We will finish by going further, by presenting the concepts of individual fairness. Finally, we will see how to correct a potential discrimination, in order to guarantee that a model is more ethical

Multiarmed Bandits Problem Under the Mean-Variance Setting

With Mario Ghossoub, Alexander Schied, and our PhD student Hongda Hu, we recently uploaded a paper entitled Multiarmed Bandits Problem Under the Mean-Variance Setting on ArXiv,

The classical multi-armed bandit (MAB) problem involves a learner and a collection of K independent arms, each with its own ex ante unknown independent reward distribution. At each one of a finite number of rounds, the learner selects one arm and receives new information. The learner often faces an exploration-exploitation dilemma: exploiting the current information by playing the arm with the highest estimated reward versus exploring all arms to gather more reward information. The design objective aims to maximize the expected cumulative reward over all rounds. However, such an objective does not account for a risk-reward tradeoff, which is often a fundamental precept in many areas of applications, most notably in finance and economics. In this paper, we build upon Sani et al. (2012) and extend the classical MAB problem to a mean-variance setting. Specifically, we relax the assumptions of independent arms and bounded rewards made in Sani et al. (2012) by considering sub-Gaussian arms. We introduce the Risk Aware Lower Confidence Bound (RALCB) algorithm to solve the problem, and study some of its properties. Finally, we perform a number of numerical simulations to demonstrate that, in both independent and dependent scenarios, our suggested approach performs better than the algorithm suggested by Sani et al. (2012).

Infectious Disease Modeling Colloquium

Save the date: Infectious Disease Modeling Colloquium, at Université de Montréal, on Jan 27, 2023, organized by CRM & Fields Institute. For registration, fill out the form (in French or in English). If you are a student/postdoc and want to give a talk/poster, pls fill out the form/submit an abstract. Partial financial support is available. Thanks Bouchra Nasri for the organization ! Jacques Bélair, Morgan Craig, Hélène Guérin (and myself) will also be involved.

Assurance collaborative, théorie des graphes et actuariat

Mardi prochain, j’interviendrais (en visio) au colloque SCOR sur le thème “Actuariat, effets réseaux et théorie des graphes

Mes slides (on m’a demandé de parler sur le thème assurance collaborative, théorie des graphes et actuariat) sont en ligne, je présenterai notre papier Collaborative Insurance Sustainability and Network Structure, mais je peux en profiter pour mentionner d’autres articles, dont modéliser la contagion, ou les réseaux pour réinventer l’assurance?