First order versus second order risk aversion

This paper defines a new concept of attitude towards risk. For an actuarially fair random variable ε{lunate}, π(t) is the risk premium the decisionmaker is willing to pay to avoid tε{lunate}. In expected utility, and as it turns out, in the case of smooth Freéchet differentiability of the representation functional, π′(0) = 0. There are models (e.g., rank dependent probabilities) in which ∂π ∂t|_t=0⁺ ≠ 0. We call the latter attitude as being of order 1, and we call the first one attitude of order 2. These concepts are then applied to analyze the problem of full insurance.