Insuring an uninsurable world – the pricing actuary’s Mission Impossible?

In InsuranceERM, David Walker published, yesterday  Insuring an uninsurable world – the pricing actuary’s Mission Impossible?

“Actuarially, it is entirely possible – and often documented – that the technical premium reflecting pure risk without political intervention, mutualisation or capping varies by a factor of 30 or more, depending on exposure to flood or forest fire risk,” says Arthur Charpentier, author of a 2024 book Insurance, Biases, Discrimination and Fairness and professor of mathematics at the Université du Québec à Montréal. This level of variation is exhibited in real life, too. Annual premiums for high-risk properties in Canadian provinces of Ontario and Alberta can exceed C$3,000 ($2,185), “compared to under C$100 elsewhere”.

In Canada, premiums are very moderate, as flood insurance is often excluded from basic policies, and “overland flood” coverage remains limited and capped (“Overland flooding … is typically not covered by a standard policy. Optional residential overland flood coverage is now offered by many insurers for the majority of homes across the country and is based on riskhttps://www.ibc.ca/stay-protected/severe-weather-safety/flood-and-water). However, technical premiums, calculated by modelers (JBA, Fathom, Swiss Re), vary by a factor of ×20 to ×50, depending on proximity to a watercourse, elevation, soil type, and flood frequency. Some properties in Ontario and Alberta have an expected annual cost of more than $3,000/year, compared to <$100 elsewhere. The report “Adapting to Rising Flood Risk” (Federal Task Force, 2022) states “Total residential flood risk in Canada… $2.9 billion per year. 89.3% is concentrated in the top 10% highest risk homes” (https://www.publicsafety.gc.ca/cnt/rsrcs/pblctns/dptng-rsng-fld-rsk-2022/index-en.aspx). This means that the most exposed minority accounts for almost all of the expected annual loss, reflecting a high degree of risk heterogeneity—the basis for justifying highly differentiated technical premiums. The same report states, “In high-risk areas, flood insurance is cost-prohibitive for Canadians, if available at all, and especially so for low-income households. In some areas, risk-based insurance premiums could reach $10,000-15,000 or more for flood endorsements alone, on top of other home insurance costs.” The actual actuarial cost is rarely passed on to the buyer, but private insurers take it into account by sometimes refusing to offer coverage or by excluding certain areas. In fact, actuarially, it is entirely possible—and often documented—that the technical premium (the one that reflects pure risk, without political intervention, mutualization, or capping) varies by a factor of ×30 or more depending on exposure to flood (or forest fire) risk. This is true in Canada, Europe, and Australia, even though this technical reality is often invisible to the insured due to political adjustment or solidarity mechanisms. For example, in France, the observed premium is uniform: 12% of the MRH contract via the CatNat scheme, regardless of the risk. But analyses show that the “real” actuarial premium could vary by a factor of 20 to 30 between a house in a non-flood zone and one in a red zone of the PPRI. Some municipalities have a loss ratio 30 times higher than the national average, but this difference is completely smoothed out. This is not the case in Germany, where flood insurance (Elementarschaden) is optional and therefore not widely mutualized. There, the commercial premium often reflects the risk more accurately, with differences of ×15 to ×30 for the most exposed areas. Three factors are often cited as reasons for this: Spatial risk heterogeneity (one neighborhood may be partially located in an area at risk of a hundred-year flood, while another, in the same zip code, is completely safe); Increase in property values (as real estate values increase (e.g., $1 million homes in coastal areas), the higher the potential capital cost, even for a low-frequency event); Changing climate and frequency (the risk is no longer stable: in Germany, Canada, and France, areas that were previously “marginal” are becoming high-risk due to climate change).

Disaster Risk Financing through Taxation: A Framework for Regional Participation in Collective Risk-Sharing

Our article Disaster Risk Financing through Taxation: A Framework for Regional Participation in Collective Risk-Sharing, written with Fallou Niakh, Caroline Hillairet and Philipp Ratz is now available !

We consider an economy composed of different risk profile regions wishing to be hedged against a disaster risk using multi-region catastrophe insurance. Such catastrophic events inherently have a systemic component; we consider situations where the insurer faces a non-zero probability of insolvency. To protect the regions against the risk of the insurer’s default, we introduce a public-private partnership between the government and the insurer. When a disaster generates losses exceeding the total capital of the insurer, the central government intervenes by implementing a taxation system to share the residual claims. In this study, we propose a theoretical framework for regional participation in collective risk-sharing through tax revenues by accounting for their disaster risk profiles and their economic status.

Collectively rethinking disasters

this post was written with Laurence Barry, initially in French

At a time when the frequency and intensity of natural disasters are increasing as a result of global warming, the issue of disaster insurance is becoming crucial to preserving economic and social resilience in most countries. However, when we look at the various existing systems, we see that the state is usually involved in one way or another in the system that has been put in place. Far from being limited to a commercial transaction between insurer and insured, insurance against natural risks takes the form of a common good—an “insurance commons”—based on mutualization, solidarity, and collective governance. To shed light on this issue and propose another framework for thinking about natural disaster insurance, we will draw on seminal work on hybrid property regimes and commons (Samuelson, 1954; Arrow, 1963; Ostrom, 1990; Ostrom & Ostrom, 1999), as well as economic analyses of insurance (Coase, 1960; Buchanan, 1965) and systemic risk management (Markowitz, 1952; Arrow & Lind, 1970). This theoretical positioning makes it possible to move beyond the traditional dichotomy between the public and private sectors, which has been further exacerbated by recent debates, to show how catastrophe insurance is in fact organized as a polycentric institution, where a multiplicity of actors—states, insurers, reinsurers, local authorities, and policyholders—have a role to play. A virtuous system is one in which all actors cooperate and regulate each other to ensure universal and effective protection despite climatic hazards. Continue reading Collectively rethinking disasters

SCOR Foundation for Science Webinar, ML and Econometrics

This week, I will give a talk at the SCOR Foundation for Science webinar (slides are available online). and I was asked to give a talk on econometrics vs IA (or machine learning),

Of course, the two concepts are related, and there is a continuum between them.

As we wrote it Charpentier et al. (2017)

Econometrics and machine learning seem to have one common goal: to construct a predictive model, for a variable of interest, using explanatory variables (or features).

For the purposes of this presentation, we will begin by contrasting the two, emphasizing the differences, and then showing the connections that exist.

Long story short, in between, we have computation statistics, or statistical learning, corresponding to computational techniques with mathematical probabilistic guarantees.

Continue reading SCOR Foundation for Science Webinar, ML and Econometrics

Causalité, pour l’Institut des Actuaires, Paris

Ce mardi, je participe en visio à la conférence annuelle de l’Institut des Actuaires, à Paris, pour une session sur les modèles causaux en assurance, avec une introduction générale, avant qu’Aurélien Couloumy ne prenne la suite pour présenter des applications.

Pour ceux qui veulent un exercice pour l’été, je peux mentionner un tableau tiré de “Optimum Strategies for Creativity and Longevity

Si quelqu’un arrive à établir un lien causal, je suis intéressé.

Beyond Shapley Values: Cooperative Games for the Interpretation of Machine Learning Models

Our paper Beyond Shapley Values: Cooperative Games for the Interpretation of Machine Learning Models, with Marouane Il Idrissi and Agathe Fernandes Machado, is now online. It will be presented at the IJCAI 2025 Workshop on Explainable Artificial Intelligence (XAI), in Montréal this Summer…

Cooperative game theory has become a cornerstone of post-hoc interpretability in machine learning, largely through the use of Shapley values. Yet, despite their widespread adoption, Shapley-based methods often rest on axiomatic justifications whose relevance to feature attribution remains debatable. In this paper, we revisit cooperative game theory from an interpretability perspective and argue for a broader and more principled use of its tools. We highlight two general families of efficient allocations, the Weber and Harsanyi sets, that extend beyond Shapley values and offer richer interpretative flexibility. We present an accessible overview of these allocation schemes, clarify the distinction between value functions and aggregation rules, and introduce a three-step blueprint for constructing reliable and theoretically-grounded feature attributions. Our goal is to move beyond fixed axioms and provide the XAI community with a coherent framework to design attribution methods that are both meaningful and robust to shifting methodological trends.