It is widely recognized that market failure prevents efficient risk sharing in natural disaster insurance, leading to several public-private partnership arrangements across the globe. We argue that risk selection, a situation where the public partner insures the majority of high risk agents, is potentially an important issue. To illustrate our concerns we build a simple model of reinsurance in a natural disaster insurance market. We show that risk selection is a likely equilibrium outcome and discuss the policy options available. The model is based on the French institutional setup and describes well the stylized facts. The policies implemented by the French government correspond to the ones we identify to alleviate risk selection. We also present two alternative public-private partnership setting that deal effectively with risk selection; hurricane insurance in Florida and catastrophe insurance in Spain.