Infrequent Extreme Risks

The main tools and cocepts of financial and actuarial theory are designed to handle standards, or even small risk. The aim of this paper is to reconsider some selected financial problems, in a setup including infrequent extreme risks. We first consider investors maximizing the expected utility function of their future wealth, and we establish the necessary of sufficient conditions on the utility function ensure the existence of a non degenerate demand for assets with extreme risk. This new class of utility function, called LIRA, does not contain the classical HARA and CARA utility functions, which are not adequate in this framework. Then we discuss the corresponding asset supply-demand equilibrium model.