## Penn Arts & Sciences

Paper # Author Title
Maximizing subjective expected utility is the classic model of decision making under uncertainty. Savage (1954) provides axioms on preference over acts that are equivalent to the existence of a subjective expected utility representation, and further establishes that such a representation is essentially unique. We show that there is a continuum of other \expected utility" representations in which the probability distributions over states used to evaluate acts depend on the set of possible outcomes of the act and suggest that these alternate representations can capture pessimism or optimism. We then extend the DM's preferences to be defined over both subjective acts and objective lotteries, allowing for source-dependent preferences. Our result permits modeling ambiguity aversion in Ellsberg's two-urn experiment using a single utility function and pessimistic probability assessments over prizes for lotteries and acts, while maintaining the axioms of Savage and von Neumann-Morganstern on the appropriate domains. Download Paper
Maximizing subjective expected utility is the classic model of decision-making under uncertainty. Savage (1954) provides axioms on preference over acts that are equivalent to the existence of a subjective expected utility representation, and further establishes that such a representation is essentially unique. We show that there is a continuum of other "expected utility" representations in which the probability distributions over states used to evaluate acts depend on the set of possible outcomes of the act and suggest that these alternate representations can capture pessimism or optimism. We then extend the DM's preferences to be defined over both subjective acts and objective lotteries, allowing for source-dependent preferences. Our result permits modeling ambiguity aversion in Ellsberg's two-urn experiment using a single utility function and pessimistic probability assessments over prizes for lotteries and acts, while maintaining the axioms of Savage and von Neumann-Morganstern on the appropriate domains Download Paper
Savage (1954) provides axioms on preferences over acts that are equivalent to the existence of a subjective expected utility representation. We show that there is a continuum of other \expected utility" representations in which for any act, the probability distribution over states depends on the corresponding outcomes and is first-order stochastically dominated by (dominates) the Savage distribution. We suggest that pessimism (optimism) can be captured by the stake-dependent probabilities in these alternate representations. We then extend the DM's preferences to be defined over both subjective acts and objective lotteries. Our result permits modeling ambiguity aversion in Ellsberg's two-urn experiment using pessimistic probability assessments, the same utility over prizes for lotteries and acts, and without relaxing Savage's axioms. An implication of our results is that the large body of existing research based on expected utility can, with a simple reinterpretation, be understood as modeling the behavior of optimistic or pessimistic decision makers. Download Paper
Savage (1954) provided axioms on preferences over acts that were equivalent to the existence of an expected utility representation. We show that there is a continuum of other expected utility" representations in which for any act, the probability distribution over states depends on the corresponding outcomes. We suggest that optimism and pessimism can be captured by the stake-dependent probabilities in these alternative representations. Extending the DM's preferences to be defined on both subjective acts and objective lotteries, we suggest how one may distinguish optimists from pessimists and separate attitude towards uncertainty from curvature of the utility function over monetary prizes. Download Paper
We propose a model of history-dependent risk attitude, allowing a decision maker’s risk attitude to be affected by his history of disappointments and elations. The decision maker recursively evaluates compound risks, classifying realizations as disappointing or elating using a threshold rule. We establish equivalence between the model and two cognitive biases: risk attitudes are reinforced by experiences (one is more risk averse after disappointment than after elation) and there is a primacy effect (early outcomes have the greatest impact on risk attitude). In dynamic asset pricing, the model yields volatile, path-dependent prices. Download Paper
Savage (1954) provided a set of axioms on preferences over acts that were equivalent to the existence of an expected utility representation. We show that in addition to this representation, there is a continuum of other expected utilityrepresentations in which for any act, the probability distribution over states depends on the corresponding outcomes. We suggest that optimism and pessimism can be captured by the stake-dependent probabilities in these alternative representations; e.g., for a pessimist, the probability of every outcome except the worst is distorted down from the Savage probability. Extending the DMs preferences to be dened on both subjective acts and objective lotteries, we show how one may distinguish optimists from pessimists and separate attitude towards uncertainty from curvature of the utility function over monetary prizes. Download Paper
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.  Download Paper
We propose a model of history dependent disappointment aversion (HDDA), allowing the attitude of a decision-maker (DM) towards disappointment 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 HDDA representation and two documented cognitive biases. First, the DM overreacts to news: after suffering a disappointment, the DM lowers his threshold for elation and becomes more risk averse; similarly, after an elating outcome, the DM raises his threshold for elation and becomes less risk averse. This makes disappointment more likely after elation and vice-versa, leading to statistically cycling risk attitudes. Second, the DM displays a primacy effect: early outcomes have the strongest effect on risk attitude. “Gray areas” in the elation-disappointment assignment are connected to optimism and pessimism in determining endogenous reference points. Download Paper