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Approximating Risk Aversion in Decision Analysis Applications. Decision Analysis
, 2004
"... Abstract This paper investigates the impact of risk aversion in decision analyses under uncertainty with a single evaluation measure and presents a simple procedure for approximately addressing risk aversion in a way that is defensible for many decisions. Speci¯cally, a simulation study is presente ..."
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Abstract This paper investigates the impact of risk aversion in decision analyses under uncertainty with a single evaluation measure and presents a simple procedure for approximately addressing risk aversion in a way that is defensible for many decisions. Speci¯cally, a simulation study is presented that leads to guidelines for determining when an expected utility analysis should be conducted for a decision, rather than simply an expected value analysis, and what form of utility function should be used for this expected utility analysis. The simulation study shows that a sensitivity analysis using an exponential utility function should be conducted for most decision analyses, but that this sensitivity analysis can often establish, without requiring utility information from the decision maker, that no further utility analysis is required. In addition, when further utility analysis is required, the simulation study shows that this can be done in a simple way using an exponential utility function that will be accurate for many decision analyses. However, in situations where there is equal or greater downside risk than upside potential a more detailed study of the decision maker's utility function may be necessary.
Learning to Make Risk Neutral Choices in a Symmetric World ∗
"... Given their reference point, most people tend to be risk averse over gains and risk seeking over losses.Therefore, they exhibit a dual risk attitude which is reference dependent. This paper considers an adaptive process for choice under risk such that, in spite of a permanent shortrun dual risk att ..."
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Given their reference point, most people tend to be risk averse over gains and risk seeking over losses.Therefore, they exhibit a dual risk attitude which is reference dependent. This paper considers an adaptive process for choice under risk such that, in spite of a permanent shortrun dual risk attitude, the agent eventually learns to make risk neutral choices.The adaptive process is based on an aspiration level, endogenously adjusted over time in the direction of the actually experienced payoff.
Nonstandard numbers for qualitative decision making (Extended Abstract)
 In: Proceedings of Seventh Conference on Theoretical Aspects of Rationality and Knowledge (TARK'98
, 1998
"... Daniel Lehmann Institute of Computer Science, Hebrew University, Jerusalem 91904, Israel lehmann@cs.huji.ac.il Abstract The consideration of nonstandard models of the real numbers and the definition of a qualitative ordering on those models provides a generalization of the principle of maxim ..."
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Daniel Lehmann Institute of Computer Science, Hebrew University, Jerusalem 91904, Israel lehmann@cs.huji.ac.il Abstract The consideration of nonstandard models of the real numbers and the definition of a qualitative ordering on those models provides a generalization of the principle of maximization of expected utility. It enables the decider to assign probabilities of different orders of magnitude to different events or to assign utilities of different orders of magnitude to different outcomes. The properties of this generalized notion of rationality are studied in the frameworks proposed by von Neumann and Morgenstern and later by Anscombe and Aumann. It is characterized by an original weakening of their postulates in two different situations: nonstandard probabilities and standard utilities on one hand and standard probabilities and nonstandard utilities on the other hand. This weakening concerns both Independence and Continuity. It is orthogonal with the weakeni...
Test Statistics for Prospect and Markowitz Stochastic Dominances with Applications
"... (SD) theory for risk averters and risk seekers by developing the prospect SD (PSD) and Markowitz SD (MSD) theory for investors with Sshaped and reverse Sshaped utility functions. Davidson and Duclos (2000) and others develop an SD test for risk averters while Wong, et al. (2007) develop an SD test ..."
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(SD) theory for risk averters and risk seekers by developing the prospect SD (PSD) and Markowitz SD (MSD) theory for investors with Sshaped and reverse Sshaped utility functions. Davidson and Duclos (2000) and others develop an SD test for risk averters while Wong, et al. (2007) develop an SD test for risk seekers. In this paper, we extend their work by developing new statistics for both PSD and MSD of the first three orders. One could then use these statistics to identify preferred assets for investors with Sshaped and reverse Sshaped utility functions. To illustrate the usefulness of our proposed statistics, we use the SD test statistics to study the preferences of investors with the corresponding Sshaped and reverse Sshaped utility functions visavis returns of traditional stocks and Internet stocks before and after the Internet bubble.
Generalized Disappointment Models
"... Based on our riskvalue framework, this paper presents generalizations and extensions for the disappointment models that were proposed by Bell (1985) and Loomes and Sugden (1986). We provide explicit functional forms for modeling the effect of disappointment on risky choice behavior. Our generalized ..."
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Based on our riskvalue framework, this paper presents generalizations and extensions for the disappointment models that were proposed by Bell (1985) and Loomes and Sugden (1986). We provide explicit functional forms for modeling the effect of disappointment on risky choice behavior. Our generalized disappointment models can explain a number of decision paradoxes, and offer additional insights into nonexpected utility preferences based on the intuitive notions of disappointment and riskvalue tradeoffs. 1 1. Introduction In our previous studies (Jia and Dyer, 1995, 1996; Dyer and Jia, 1997), we proposed riskvalue models such that decisions can be made based on the intuitively appealing idea of riskvalue tradeoffs. We demonstrated that these riskvalue models are very flexible in modeling preferences, and provide new resolutions for observed risky choice behavior and some decision paradoxes. Let X be a random variable representing a lottery, and X the mean of that lottery; then X'...
Binary Gambles of a Gain and a Loss: an Understudied Domain
"... Assume that binary rankdependent expected utility (subjective expected utility is a special case) holds for gains and losses separately and that a commutative binary operation of joint receipt on consequences and gambles is linked to binary gambles via the rational property of segregation. This imp ..."
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Assume that binary rankdependent expected utility (subjective expected utility is a special case) holds for gains and losses separately and that a commutative binary operation of joint receipt on consequences and gambles is linked to binary gambles via the rational property of segregation. This implies that utility U of joint receipt is either itself additive or is an exponential transformation of an additive representation V. For joint receipt of mixed gains and losses two hypotheses are discussed: either U or V is additive over mixed joint receipts. Both hypotheses are linked back to gambles in two different ways: a generalization of segregation and an empirically sustained but nonrational property called duplex decomposition. The additive U model yields bilinear expressions like rankdependent expected utility. Data favor the latter. The additive V models yield nonbilinear representations of mixed gambles.
Risk and Hedging Behavior: The Role and Determinants of Latent Heterogeneity. The Journal of Financial Research (forthcoming
, 2009
"... Risk and hedging behavior: The role and determinants of latent heterogeneity ..."
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Risk and hedging behavior: The role and determinants of latent heterogeneity
2004), “Attitudes on Gain and Loss Lotteries: A Simple Experiment,” Discussion Paper 0402, School of Economic Studies
"... Abstract: A new definition of loss aversion is proposed and tested. Thirtyone students participated in experiments on lotteries involving small scale real gains and losses. At the aggregate level, approximately 60 % of the choices are in the direction of loss aversion. The analysis at the individua ..."
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Abstract: A new definition of loss aversion is proposed and tested. Thirtyone students participated in experiments on lotteries involving small scale real gains and losses. At the aggregate level, approximately 60 % of the choices are in the direction of loss aversion. The analysis at the individual level shows that, compared to loss seekers, more than twice as many are loss averters, the remaining subjects being unclassified. Comparing these results with risk behavior involving gain only lotteries shows a strong polarization effect: when loss outcomes are introduced, a majority of subjects shift from unclassified risk attitude in the domain of gains towards loss aversion, but some exhibit loss seeking. A strong gender effect is also observed. Proportionally more women are sensitive to losses. There is statistical evidence that in these binary choices the sign of common outcomes has influence on choice behavior, which is in contrast to the predictions of comonotonic independence, the core principle of rankdependent utility theories.
TOWARD AN INTEGRATED PRACTICE OF BEHAVIORAL CONFLICT MANAGEMENT
, 2003
"... Conflict resolution is about decision making. Because decision outcomes for conflicting parties depend, at least to some extent, on the decisions of other parties to the conflict, as well as a multitude of external circumstances and third party decision making, these decisions are always made under ..."
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Conflict resolution is about decision making. Because decision outcomes for conflicting parties depend, at least to some extent, on the decisions of other parties to the conflict, as well as a multitude of external circumstances and third party decision making, these decisions are always made under conditions of uncertainty or risk. Conflict management is about guiding this decision making in such a manner as to mitigate this risk to the greatest extent possible. Expected utility and subjective expected utility have contributed to the development of a normative theory of decision making under uncertainty that is economically maximizing, with possible allowances for differently shaped utility curves. On the other hand, substantial empirical efforts have contributed descriptive theories of decision making under uncertainty that attempt to address departures from the purely rational model – departures that importantly often prove to be quite robust and predictable across a wide range of decision making contexts. This Essay proposes an agenda for conflict management research that seeks to leverage both the rational expectation models and the behavioral theories describing predictable deviations from these models to arrive at prescriptions for conflict management practice that can build a bridge between theory and practice, offering practical techniques and concrete guidelines for improvement. Specific ways that these insights can contribute to the development of conflict management practice are considered.
Prospect and Markowitz Stochastic Dominance
, 2005
"... Levy and Levy (2002, 2004) develop the Prospect and Markowitz stochastic dominance theory with Sshaped and reverse Sshaped utility functions for investors. In this paper, we extend Levy and Levy’s Prospect Stochastic Dominance theory (PSD) and Markowitz Stochastic Dominance theory (MSD) to the fir ..."
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Levy and Levy (2002, 2004) develop the Prospect and Markowitz stochastic dominance theory with Sshaped and reverse Sshaped utility functions for investors. In this paper, we extend Levy and Levy’s Prospect Stochastic Dominance theory (PSD) and Markowitz Stochastic Dominance theory (MSD) to the first three orders and link the corresponding Sshaped and reverse Sshaped utility functions to the first three orders. We also provide experiments to illustrate each case of the MSD and PSD to the first three orders and demonstrate that the higher order MSD and PSD cannot be replaced by the lower order MSD and PSD. Prospect theory has been regarded as a challenge to the expected utility paradigm. Levy and Levy (2002) prove that the second order PSD and MSD satisfy the expected utility paradigm. In our paper we take Levy and Levy’s results one step further by showing that both PSD and MSD of any order are consistent with the expected utility paradigm. Furthermore, we formulate some other properties for the PSD and MSD including the hierarchy that exists in both PSD and MSD relationships; arbitrage opportunities that exist in the first orders of both PSD and MSD; and that for any two prospects under certain conditions, their third order MSD preference will be ‘the opposite ’ of or ‘the same’ as their counterpart third order PSD preference. By extending Levy and Levy’s work, we provide investors with more tools for empirical analysis, with which they can identify the first order PSD and MSD prospects and discern arbitrage opportunities that could increase his/her utility as well as wealth and set up a zero dollar portfolio to make huge profit. Our tools also enable investors to identify the third order PSD and MSD prospects and make better choices.