Evidence such as the Ellsberg Paradox shows that decision-makers do not assign probabilities to all events. It is intuitive that they may differ not only in the probabilities assigned to given events but also in the identity of the events to which they assign probabilities. This paper describes a theory of probability that is fully subjective in the sense that both the domain and the values of the probability measure are derived from preference. The key is a formal definition of `subjectively unambiguous event.'

The Pratt-Arrow measure of local risk aversion is generalized for the n-dimensional state-preference model of choice under uncertainty in which the decision maker may have inseparable subjective probabilities and utilities, unobservable stochastic prior wealth, and/or smoothnonexpected-utility preferences. Local risk aversion is measured by the matrix of derivatives of the decision maker’s risk-neutral probabilities, without reference to true subjective probabilities or riskless wealthpositions, and comparative risk aversion is measured without requiring agreement on true probabilities. Risk-neutral probabilities and their derivatives are shown to be sufficient statistics for approximately optimal investment and financing decisions in complete markets for contingent claims.

This paper examines qualitative properties of efficient insurance contracts in the presence of background risk. In order to get results for all strictly risk averse expected utility maximizers, the concept of “stochastic increasingness ” is used. Different assumptions on the stochastic dependence between the insurable and uninsurable risk lead to different qualitative properties of the efficient contracts. The new results obtained under hypotheses of dependent risks are compared to classical results in the absence of background risk or to the case of independent risks. The theory is further generalized to nonexpected utility maximizers. Key words: insurance, efficient contracts, incomplete markets, stochastically increasing. JEL Classification: D52, G22. 1

We consider the problem of efficient insurance contracts when the cost structure includes a fixed cost per claim. We define and show existence of "continuous-Pareto efficient contracts" and prove that every Pareto efficient contract is utility equivalent to some continuous-Pareto efficient contract. We establish that continuous-efficient contracts have standard properties. The concept is then applied to two models of deterministic auditing with different information structures. 1 Introduction Since Borch [4] and Arrow's early work [1, 2] the design of efficient insurance contracts has received a lot of attention. Arrow's original result that full coverage of the loss above a deductible is optimal when the insured is risk averse and the insurer risk neutral with linear cost has been generalized to many settings : risk averse insurer, convex costs, non expected utility maximizers, etc... Two lines of research are of particular interest to our paper. Townsend [17] elaborates on Radner's ...

We propose a notion of smoothness of nonexpected utility functions, which extends the variational analysis of nonexpected utility functions to more general settings. In particular, our theory applies to state dependent utilities, as well as the multiple prior expected utility model, both of which are not possible in previous literatures. Other nonexpected utility models are shown to satisfy smoothness under more general conditions than the Fréchet and Gateaux differentiability used in the literature. We give more general characterizations of monotonicity and risk aversion without assuming state independence of utility function. Ai, University of Minnesota and Federal Reserve Bank of Minneapolis. I thank Michele Boldrin for his advice and continuous encouragement. I thank David Levine for helpful comments. All errors are mine. The views expressed herein are those of the author and not necessarily those of the Federal Reserve Bank of Minneapolis or the

Abstract: This paper develops a methodology for characterizing expected revenue from auctions in which bidders ’ types come from an arbitrary distribution. In particular, types may be multidimensional, and there may be mass points in the distribution. One application extends existing revenue equivalence results. Another application shows that first-price auctions yield higher expected revenue than second-price auctions when bidders are risk averse and/or face financial constraints. This revenue ranking also extends to risk-averse bidders with general forms of non-expected utility preferences.

Abstract: This paper develops a methodology for characterizing expected revenue from auctions when bidders ’ types come from an arbitrary distribution. In particular, types may be multidimensional, and there may be mass points in the distribution. One application extends existing revenue equivalence results. Another application shows that first-price auctions yield higher expected revenue than second-price auctions when bidders are risk averse and face financial constraints. This revenue ranking extends to risk-averse bidders with general forms of non-expected utility preferences.

We propose a model of history-dependent risk attitude (HDRA), allowing the attitude of a decision-maker (DM) towards risk at each stage of a T-stage lottery to evolve as a function of his history of disappointments and elations in prior stages. We establish an equivalence between the existence of an HDRA representation and two documented cognitive biases. First, the DM’s risk attitudes are reinforced by prior experiences: he becomes more risk averse after suffering a disappointment and less risk averse after being elated. Second, the DM displays a primacy effect: early outcomes have the strongest effect on risk attitude. Furthermore, the DM lowers his threshold for elation after a disappointing outcome and raises it after an elating outcome; this makes disappointment more likely after elation and vice-versa, leading to statistically reversing risk attitudes. “Gray areas ” in the elation-disappointment assignment are connected to optimism and pessimism in determining endogenous reference points.