AbstractOur concern is with protection against natural catastrophes through financial insurance. Development of appropriate premium rates requires consideration of a wide variety of variables entering into the occurrence of the disaster, and a broad range of scientific and statistical investigations results. Topics discussed include: premium computation, distribution of large earthquakes in time, ground motion at sites, attenuation of energy with distance, damage description and actual practice in various countries. Statistical considerations that arise include: description, stochastic modelling, conditioning, spatial processes, (marked) point processes, uncertainty estimation and robust/resistant procedures. Study of the insurance problem is scientifically enlightening because it requires one to focus on the whole context of the problem; geology, seismology, earthquake engineering, and damage.