Essays on risk aversion

This dissertation contains three essays on risk aversion. In the first essay, we an-alyze comparative risk aversion in a new way, through a comparative statics problemin which, for a cost, agents can shift from an initial probability distribution towarda preferred distribution. The Ross characterization arises when the original distribution is riskier than the preferred distribution and the cost is monetary, and theArrow-Pratt characterization arises when the original distribution differs from thepreferred distribution by a simple mean-preserving spread and the cost is a utilitycost. Higher-order increases in risk lead to higher-order generalizations, and the com-parative statics method yields a unified approach to the problem of comparative riskattitudes.In the second essay, we analyze decisions made by a group of terrorists and agovernment in a zero-sum game in which the terrorists minimize a representativecitizen's expected utility and the government maximizes it. The terrorists' strategybalances the probability and the severity of the attack while the government choosesthe level of investment reducing the probability and/or mitigating the severity. Wefind that if the representative citizen is risk neutral, the terrorists' response is notassociated with the government's action and the representative citizen's risk attitudesaffect the strategies of the government and the terrorists. Risk aversion always in-creases equilibrium severity but does not always increase equilibrium expenditure of the government.In the last essay, we consider a situation in which an individual has to pay fora good before he realizes the state-dependent surplus of the good. This ex-antewillingness to pay is called the option price and the difference between the optionprice and the expected surplus is the option value. We find that the option valueactually is the buying price for a fixed payment of the expected surplus, and there isa special case in which the option value equals the negative of the compensating riskpremium. We also find the effects on the option price and the option value when theexpected utility assumption is replaced by a rank-dependent expected utility.