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Insurance against natural catastrophes: balancing actuarial fairness and social solidarity

Abstract

Natural disasters offer a specific case study of the mix of public and private insurance. Indeed, the experience accumulated over the past decades has made it possible to transform poorly-known hazards like flood losses, long considered uninsurable, into risks that can be assessed with some precision. They exemplify, however, the affordability issue associated with risk-based premiums. The French scheme reflects such ideas and offers wide coverage for moderate premiums to all, but is questioned in its principle by climate change: we show that some wealthier areas that were not perceived as ‘at risk’ in the past have now become exposed to submersion risk. This singularly makes some well-off properties the potential main beneficiaries of a scheme that was historically thought to protect the worst-off. Acknowledging that some segmentation may become desirable, we examine several models for flood risk and the disparity in premiums they entail.

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Notes

  1. In this article, we use state to designate a nation-based collective action, as in Scott (1998). The word government, as in Moss (2002), was considered, but we will use state as consistently as possible.

  2. Even if premiums asked by insurance companies would be based on several risk-related variables, we only consider here the location of the house or apartment.

  3. The system covers most natural disasters, so geographic diversity increases the chance of facing at least one specific risk in a given area. Nevertheless, in this article, we will not take into account this possible diversification and focus only on the largest in France, flood risk.

  4. In practice, the 5.5% appeared insufficient the next year and was raised to 9%. In 1999, the loading was raised again to its current level of 12%.

  5. Reinsurance is optional. However, since the CatNat premium is fixed by decree, almost all insurers are currently reinsured with the public reinsurer.

  6. Via http://www.vendee.gouv.fr/approbation-du-pprl-de-la-baie-de-bourgneuf-vendee-a2200.html.

  7. This contention was further questioned in the literature (see for instance Ericson and Doyle 2004; O’Malley 2003; Collier 2008), but this discussion is out of the scope of this paper.

  8. For a historical description of the system with a focus on Florida see Michel-Kerjan and Kousky (2010).

  9. Further studies led to a threshold of unaffordability when insurance premiums exceed 1% of income (Long 2018; see also National Research Council 2015). While estimating the threshold of affordability is of interest from the perspective of this paper, the comparison with the U.S. should be handled with care: indeed, the U.S. flood programme is plagued by adverse selection due to low take up. Consequently, recommendations for improving the affordability of the U.S. flood programme may not be directly relevant to the French programme.

  10. The details for several towns are given in Table 8 in the Appendix, and maps are available as supplementary material online at https://github.com/freakonometrics/floods.

  11. The municipality of La Faute-sur-Mer became famous since 29 people died at the end of February 2010 because of the coastal flood caused by windstorm Xynthia.

  12. It started at 5.5%, jumped to 9% in 1985, and then to 12% in 2000.

  13. We will mention here only household insurance, not commercial buildings.

  14. We use here the word town to designate a ‘commune’ or municipality.

  15. From https://www.insee.fr/fr/statistiques/3126432.

  16. From https://www.insee.fr/fr/statistiques/4171418?sommaire=4171436.

  17. From https://www.insee.fr/fr/statistiques/1906666?sommaire=1906743.

  18. https://cadastre.data.gouv.fr/dvf.

  19. E.g. for the département of Eure, in Normandy https://www.data.gouv.fr/fr/datasets/perimetres-des-plans-de-prevention-du-risque-inondationdans-leure.

  20. The fact that \(15{\%}\) of the households are experiencing about \(90{\%}\) of the losses, over 20 years, is actually not unusual in insurance: if we assume that flood risk is uniform and centennial (each household has a 1% yearly chance of claiming a loss), and that all risks are independent, then over 20 years \(18.2{\%}\) of the households claim a loss at least once—if X has a binomial distribution \(\mathcal {B}(n=20,p=1{\%})\) (since we assure independence between years) then \(\mathbb {P}(X=0)=(1-p) ^n=0.99^{20}=81.79{\%}\). So, 100% of the losses are related to \(18.2{\%}\) of the portfolio (and possibly \(18.2{\%}\) is the premium earned).

  21. The Will Rogers phenomenon is obtained when moving an element from one set to another set raises the average values of both sets. It is based on the quote, attributed to comedian Will Rogers, when the Okies left Oklahoma and moved to California, they raised the average intelligence level in both states.

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Acknowledgements

The authors wish to thank the two anonymous referees for numerous and very helpful comments and suggestions, as well as Wouter Botzen, Thierry Cohignac, Pierre François, Arnaud Goussebaille, Burrell Montz and Pierre Picard for discussions and feedback on a previous version of this text. Arthur Charpentier received financial support from NSERC and the AXA Research Fund.

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Appendix

Appendix

Prices of houses and apartments in towns with PPRL (coastal risk) in Vendée and Loire-Atlantique

Table 8 Prices (EUR per \(m^2\)) of houses sold (2000–2020) in several towns in Pays de la Loire and Vendée—Western part of France, with PPRL (coastal risk)

Prices of houses and apartments in towns with PPRI (overflow risk) in Var

Table 9 Prices (EUR per \(m^2\)) of houses sold (2000–2020) in several towns in the Var departement, in France, with PPRI (overflow coastal)

Premiums with the hierarchical model

In Tables 6 and 7, we considered some arbitrary values for the pair \((\gamma ,\beta )\), with \(\gamma \in \{0{\%},20{\%},40{\%}\}\) and \(\beta \in \{10{\%},20{\%},50{\%}\}\) (as well as some extreme cases in \(\{0{\%},100{\%}\}\)). In Fig. 8, we have the level curves of premiums as a function of \(\gamma\) and \(\beta\) (or iso-premium curves), where \(\gamma\) is the share of national solidarity and \((1-\gamma )\beta\) is the share of municipality-based solidarity. The key point here is that there is no universal or general pattern. The evolution of the premium \((\beta ,\gamma )\mapsto p_{i:j}(\beta ,\gamma )\) depends on the city i, its relative risk level in its region j and the relative risk level in the country.

Fig. 8
figure 8

Iso-premiums \(p(\beta ,\gamma )\) (in %) for nine towns, for different values of \(\gamma\) and \(\beta\). The vertical line on the right (\(\gamma =1\)) corresponds to the benchmark case, with \(p=6.8{\%}\)

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Charpentier, A., Barry, L. & James, M.R. Insurance against natural catastrophes: balancing actuarial fairness and social solidarity. Geneva Pap Risk Insur Issues Pract 47, 50–78 (2022). https://doi.org/10.1057/s41288-021-00233-7

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Keywords

  • Natural disasters
  • Actuarial fairness
  • Solidarity
  • Climate change
  • Flood
  • France