Coward Behaviour and First-Order Risk Aversion

According to a revised definition of Samuelson, a risk-averse agent is called a coward whenever he refuse even a small portion of a risky gamble exhibiting a positive expected payoff. This property may cause the invalidation of some of the basic theorems of the insurance and finance theory. As recently pointed out by Segal and Spivak (1990), risk aversion of the first order is a sufficient condition for that. Nevertheless, the attitude toward the risk is not the only culprit of the classical result failure, since the latter depends also on the distribution of the risky gamble. By properly balancing restrictions over these two gears, conditions for guaranteeing the desired attitude are set out. A number of examples illustrate their applicability