Insurance is a classical tool to hedge against risks. Thanks to the law of large numbers, it pools funds from a large number of similar exposures to pay for the losses incurred by somehow. The theory tells us that all risk-adverse people is willing to buy insurance if the premium is actuarially fair or even if the price of the coverage is greater than the expected loss. However, what happens in the insurance market of catastrophic risks is completely different: demands for cat covers, subscribed voluntarily, are rare. Paying a premium for a risk with low probability but high loss, even if it is fair, is considered an overprotection. This is probably due to incomplete information. This irrationality in the demand does not allow insurance firms to reach the critical mass, necessary to define the right capital allocation. This is one of the reasons why cat covers are not so widespread in the insurance market. In the present paper, we investigate the anomalous behaviour of demand and supply for cat policies and we study some possible solutions. We focus on the Italian flood risks insurance market and we illustrate the critical aspects of the evaluation and rate making process under an actuarial point of view. Keywords: Anomalous behaviours, Demand and Supply, Insurance market, Catastrophic risks, Pricing and Hedging.