Category Archives: Publications

Collaborative Insurance Sustainability and Network Structure

A second version of Collaborative Insurance Sustainability and Network Structure is now available on ArXiv,

The peer-to-peer (P2P) economy has been growing with the advent of the Internet, with well known brands such as Uber or Airbnb being examples thereof. In the insurance sector the approach is still in its infancy, but some companies have started to explore P2P-based collaborative insurance products (eg. Lemonade in the U.S. or Inspeer in France). The actuarial literature only recently started to consider those risk sharing mechanisms, as in Denuit and Robert (2021) or Feng et al. (2021). In this paper, describe and analyse such a P2P product, with some reciprocal risk sharing contracts. Here, we consider the case where policyholders still have an insurance contract, but the first self-insurance layer, below the deductible, can be shared with friends. We study the impact of the shape of the network (through the distribution of degrees) on the risk reduction. We consider also some optimal setting of the reciprocal commitments, and discuss the introduction of contracts with friends of friends to mitigate some possible drawbacks of having people without enough connections to exchange risks.

Les biais, les discriminations et l’équité en assurance

Sur Variances, un court article pour présenter le rapport remis au début de l’été à l’Institut Louis Bachelier, Assurance : Discrimination, biais et équité.

Les données massives et les performances obtenues par les algorithmes d’apprentissage automatique ont chamboulé l’assurance et l’actuariat. Les questions soulevées par ces nouveaux outils dans d’autres contextes (que ce soit la justice prédictive (ou justice “actuarielle” comme l’appelle Harcourt (2008)) ou les débats sur les fake news, en passant par les véhicules autonomes et la médecine prédictive) poussent les actuaires au doute, et à la méfiance. Kranzberg (1986) affirmait que “technology is neither good nor bad; nor is it neutral”, mettant en avant que, même sans mauvaises intentions, les algorithmes d’apprentissage pouvaient être injustes. Et corriger ces possibles injustices n’est pas simple. Pour Nielsen (2020), “technology does not necessarily self-regulate, via either market or social pressures” (la main invisible des marchés ou de la pression sociale ne suffira peut être pas). C’est dans ce contexte que nous allons revenir ici sur les problématiques de biais, de discrimination et d’équité, des modèles prédictifs utilisés en assurance. Ces changements, tant sur les données que sur les modèles, que l’on observe depuis une petite dizaine d’années, avaient déjà questionné l’existence même de l’assurance (à suivre).

What is the future of predictive probabilities in insurance?

This post was written with Laurence Barry and Ewen Gallic, in French, in November 2019 (see hal-02350006)

Insurance policies are classic examples of random contracts. This forces insurers to regularly quantify this uncertainty, to calculate probabilities in order to propose “fair” premiums for the commitments they are going to make. Isn’t it time to question this practice, at a time when artificial intelligence is exploding, offering predictive algorithms of a precision never seen before? At a time when big data / big brother could mean the disappearance of uncertainty itself?
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On consequences of Goodhart’s law

This post was initially written in French, in the Winter 2021.

As Marilyn Strathern stated, Goodhart’s Law says that “when a measure becomes a goal, it ceases to be a good measure.” There are many economic applications, but this law also helps to understand the dangers of algorithmic decisions, or to explain the difficulty of using the data available since the beginning of the SARS-CoV-2 COVID-19 pandemic.

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The scientific approach in times of crisis

This post was initially written in French, and published in April 2020.

In a conference given on February 13, 2020[i], entitled Against the Method, Didier Raoult stated “I have never done randomized trials […] to do that on infectious diseases, it makes no sense“. This view was repeated in a more detailed article, where Didier Raoult defended (what he called) “the morality [and] the humanism” of the Hippocratic oath against “the method” (and “mathematics”). As he reminds us, doing control groups is “telling the patient that we are going to give him at random either the drug we know works or the drug we do not know works” (Raoult (2020a, 2020b)). While this method of randomized experiments is now hailed in all disciplines – as the Nobel Prize in Economics awarded in 2019 to Esther Duflo, Michael Kremer and Abhijit Banerjee reminds us – how can a researcher take such a position today?
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Government Intervention in Catastrophe Insurance Markets

Our paper, Government Intervention in Catastrophe Insurance Markets: A Reinforcement Learning Approach, jointly written with Menna Hassan and Nourhan Sakr is now available on ArXiv.

This paper designs a sequential repeated game of a micro-founded society with three types of agents: individuals, insurers, and a government. Nascent to economics literature, we use Reinforcement Learning (RL), closely related to multi-armed bandit problems, to learn the welfare impact of a set of proposed policy interventions per $1 spent on them. The paper rigorously discusses the desirability of the proposed interventions by comparing them against each other on a case-by-case basis. The paper provides a framework for algorithmic policy evaluation using calibrated theoretical models which can assist in feasibility studies.

What responsibility for the algorithms?

This post was initially written in French with Rodolphe Bigot (lecturer at the University of Picardie Jules Verne), in the Winter 2020, and follows a previous post entitled Rethinking responsibility and causality.

Historically, algorithms were content to provide decision support, leaving a human being to make the decision, but experiments are underway, with autonomous systems, making decisions, whether it be car driving systems, or predictive justice algorithms, as shown by Huss et al. (2018). This autonomy, which basically means the “ability to act freely” also refers to the idea of “governing oneself by one’s own laws“. But what is the responsibility of the decision maker in the case of a prediction that leads to harm?
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Insurance and discrimination, what role for actuaries?

This post was initially published in French in September 2021.

The essential role of an actuary in charge of pricing is the segmentation of the portfolio (or “insurance classification” in English), corresponding to a discrimination activity (mathematically speaking) in the sense that the actuary will look for the most “discriminating” variables, to explain another one (in relation with the loss experience). But in the legal sense, discrimination is forbidden by law, which places the actuary in an often delicate and complex position.
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The myth of interpretability and explicability of models

This article was initially written in French and published in November 2021.

Rubinstein (2012) claimed that “in economic theory, like Harry Potter, the Emperor’s New Clothes, or King Solomon’s Tales, we play in imaginary worlds. Economic theory invents tales and calls them models. An economic model is also somewhere between fantasy and reality (…) The word ‘model’ sounds more scientific than the word ‘fable’ or ‘tale’, but I think we are talking about the same thing“. Today, very often, learning models will build a model, based on learning data, and the actuary’s job will be to make sense of it, to find the story – the fable – that it is possible to tell. Continue reading The myth of interpretability and explicability of models

Reconciling collective risks and individual decisions

This article was co-authored with Laurence Barry, and initially written in French during the 2020 Summer.

The early days of the SARS-CoV-2 (or COVID-19) pandemic have seen a proliferation of calls for “individual responsibility”, starting with strong calls (and even an obligation in some countries, including France) to stay home as much as possible in the early spring of 2020, before it became mandatory to wear a mask in public (often closed) places during the summer. To paraphrase Coluche « dire qu’il suffirait que les gens restent chez eux pour qu’on puisse sortir… ». This call for each person’s responsibility is made in the name of all and for the good of all, symbolizing this very particular solidarity that the pandemic reminds us of: the risk that I choose to run does not only concern my person but also constitutes a risk for those around me. To formulate it in probabilistic terms, McKendrick (1926) stated that “the probability of occurrence increases with the number of existing cases“. This conception of individual responsibility, which is quite intuitive a priori, actually runs counter to the classical conception of economics: the rational (and responsible) individual makes choices that concern him, and that concern only him. The collective good is deduced by summing up individual utilities, independent of each other. But here is the problem: with the epidemic, an interdependence of utilities is created, so that the well-being of so-and-so, who chooses not to wear a mask, can harm the health and therefore the utility of many other people. How then can we think in economic terms of this “individual responsibility” in the context of the epidemic?

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The taboo of the exponential

For Carl Sagan, “if you understand exponentials, the key to many of the secrets of the universe is in your hand”. But not everyone seems ready to unlock the secrets of the universe. Thus, in mid-November 2021, more than 18 months after the beginning of the SARS-COVID 19 pandemic, the Minister of Health stated “the circulation of the virus has accelerated for a few weeks now, with an increase of 30% to 40% per week. We are not yet in a so-called exponential phase” (quoted in Ouest France (2021)). Since an increase at a constant rate is precisely the definition of “exponential growth”, one may wonder about this statement, which reveals either a lack of numeracy on the part of our leaders, or an element of language, with the word “exponential” becoming a taboo word that should not be mentioned?

(this is the English tranlation of a post published in January 2022)

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Modeling contagion

Two years after the beginning of the COVID-19 pandemic, due to the SARS-CoV-2 virus, we have all become (pseudo)-experts in contagion models. But beyond diseases, these models based on networks of interactions between people are also commonly used to describe the spread of a computer virus, of social norms, of an idea or a rumor in a society, or of an economic crisis, as Kucharski (2020) reminds us.

(this is the English tranlation of a post published in April 2022)

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Are there acceptable deaths? or how to end a pandemic

Zylberman (2021) noted that “this pandemic began with the first case, but it will not end with the last case (…) one cannot date the end of a pandemic and the beginning of an endemic. Yet, in mid-April, the French president slipped in an interview (Garnier (2022)) that “society [is] on its way out of COVID” implying that the SARS-CoV-2 pandemic was over. At the same time, the virus was still killing more than 100 people a day, according to official statistics. While it is legitimate to question what exactly is a “COVID death“, it may seem surprising that 100 deaths per day (for more than three consecutive months) were met with such indifference, and that such a level was interpreted as the end of the pandemic.

(this is the English translation of a blog post published a few days ago)
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