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.

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

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 $p=6.8{\%}$