In this talk, after looking back at previous work done in the context of climate risk (discussing temporal dynamics and occurrence of multiple catastrophes in a given year), we will review two recent studies. The first one, Insurance against natural catastrophes: balancing actuarial fairness and social solidarity, about flood risk in France, looks at the fairness of the French "natural catastrophes" mechanism, in the context of climate change (and the increase of coastal risk). The second one, Predicting Drought and Subsidence Risks in France, we discuss prediction of subsidence risk in France, using various statistical models. Finally, we will (briefly) present two ongoing projects, the first one on wildfires and the second one on the optimal intervention of government in the context of catastrophes.