Ruin problem in a changing environment and application to the cost of climate change for an insurance company.

Summary In this paper we obtain asymptotics for ruin probability in a risk model where claim size distribution as well as claim frequency change over time. This is a way to take into account observed and/or projected changes, due to climate change, in some specific weather-related events like tropical storms for instance. Some examples will be presented in order to illustrate the theory and start a discussion on the possible cost of climate change for an insurance company who wants to remain financially solvent.