A General Theorem on the Comparative Statics of Changes in Risk

In this paper, the concept of “absolutely riskier than” is introduced to generalize Gollier's (Journal of Economic Theory, 66, 522–535) necessary and sufficient conditions for the comparative statics of a change in risk for risk averters. The restrictive assumption that the payoff function is monotonic in the risk is relaxed. The “policymaker's choice problem,” the “newsboy problem,” and a farmer's example are used to illustrate how easily the monotonicity assumption is violated. Finally, some important properties of the concept of “absolutely riskier than,” such as its relation with the concept of “second-order stochastic dominance,” are illustrated using the farmer's example.