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on Utility Models and Prospect Theory |
| By: | Ghossoub, Mario |
| Abstract: | This paper suggests a behavioral, preference-based definition of loss aversion for decision under risk. This definition is based on the initial intuition of Markowitz [30] and Kahneman and Tversky [19] that most individuals dislike symmetric bets, and that the aversion to such bets increases with the size of the stake. A natural interpretation of this intuition leads to defining loss aversion as a particular kind of risk aversion. The notions of weak loss aversion and strong loss aversion are introduced, by analogy to the notions of weak and strong risk aversion. I then show how the proposed definitions naturally extend those of Kahneman and Tversky [19], Schmidt and Zank [48], and Zank [54]. The implications of these definitions under Cumulative Prospect Theory (PT) and Expected-Utility Theory (EUT) are examined. In particular, I show that in EUT loss aversion is not equivalent to the utility function having an S shape: loss aversion in EUT holds for a class of utility functions that includes S-shaped functions, but is strictly larger than the collection of these functions. This class also includes utility functions that are of the Friedman-Savage [14] type over both gains and losses, and utility functions such as the one postulated by Markowitz [30]. Finally, I discuss possible ways in which one can define an index of loss aversion for preferences that satisfy certain conditions. These conditions are satisfied by preferences having a PT-representation or an EUT-representation. Under PT, the proposed index is shown to coincide with Kobberling and Wakker’s [22] index of loss aversion only when the probability weights for gains and losses are equal. In Appendix B, I consider some extensions of the study done in this paper, one of which is an extension to situations of decision under uncertainty with probabilistically sophisticated preferences, in the sense of Machina and Schmeidler [27]. |
| Keywords: | Loss Aversion; Risk Aversion; Mean-Preserving Increase in Risk; Prospect Theory; Probability Weights; S-Shaped Utility |
| JEL: | D03 D81 |
| Date: | 2011–08–11 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:37628&r=upt |
| By: | Mark Dean; Pietro Ortoleva |
| Abstract: | We study the relation between ambiguity aversion and the Allais paradox. To this end, we introduce a novel denition of hedging which applies to objective lotteries as well as to uncertain acts, and we use it to dene a novel axiom that captures a preference for hedging which generalizes the one of Schmeidler (1989). We argue how this generalized axiom captures both aversion to ambiguity, and attraction towards certainty for objective lotteries. We show that this axiom, together with other standard ones, is equivalent to to two representations both of which generalize the MaxMin Expected Utility model of Gilboa and Schmeidler (1989). In both, the agent reacts to ambiguity using multiple priors, but does not use expected utility to evaluate objective lotteries. In our rst representation, the agent treats objective lotteries as `ambiguous objects,' and use a set of priors to evaluate them. In the second, equivalent representation, lotteries are evaluated by distorting probabilities as in the Rank-Dependent Utility model, but using the worst from a set of such distortions. Finally, we show how a preference for hedging is not sucient to guarantee an Ellsberg-like behavior if the agent violate expected utility for objective lotteries. We then provide an axiom that guarantees that this is the case, and nd an associated representation in which the agent rst maps acts to an objective lottery using the worst of the priors in a set; then evaluates this lottery using the worst distortion from a set of concave Rank-Dependent Utility functionals. |
| Keywords: | Ambiguity Aversion, Allais Paradox, Ellsberg Paradox, Hedging, Multiple Priors, Subjective Mixture, Probability Weighting, Rank Dependent Expected Utility |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:bro:econwp:2012-2&r=upt |
| By: | Napp, Clotilde; Jouini, Elyès |
| Abstract: | In this paper, we show that behavioral features can be obtained at a group level when the individuals of the group are heterogeneous enough. Starting from a standard model of Pareto optimal allocations, with expected utility maximizers but allowing for heterogeneity among individual beliefs, we show that the representative agent has an inverse S-shaped probability distortion function. As an application of this result, we show that an agent with a probability weighting function as in Cumulative Prospect Theory may be represented as a collection of agents with noisy beliefs. |
| Keywords: | probability weighting function; ambiguity aversion; behavioral agent; representative agent; |
| JEL: | D81 G11 D84 D87 D03 |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:ner:dauphi:urn:hdl:123456789/4723&r=upt |
| By: | Lefort, Jean-Philippe; Dominiak, Adam; Dürsch, Peter |
| Abstract: | Two rationality arguments are used to justify the link between conditional and unconditional preferences in decision theory : dynamic consistency and consequentialism. Dynamic consistency requires that ex ante contingent choices are respected by up dated preferences. Consequentialism states that only those outcomes which are still possible can matter for up dated preferences. We test the descriptive validity of these rationality arguments with a dynamic version of Ellsberg's three color experiment and that subjects act more often in line with consequentialism than with dynamic consistency. |
| Keywords: | experiment; consequentialism; dynamic consistency; updating; ambiguity; Non expected utility preferences; |
| JEL: | D81 C91 |
| Date: | 2012–01 |
| URL: | http://d.repec.org/n?u=RePEc:ner:dauphi:urn:hdl:123456789/7357&r=upt |
| By: | Carvalho, M. (Tilburg University, Center for Economic Research) |
| Abstract: | Abstract: This paper presents the outcome of a dynamic price-descending auction when the distribution of the private values is uncertain and bidders exhibit ambiguity aversion. In contrast to sealed-bid auctions, in open auctions the bidders get information about the other bidders' private values and may therefore update their beliefs on the distribution of the values. The bidders have smooth ambiguity preferences and update their priors using consequentialist Bayesian updating. It is shown that ambiguity aversion usually affects bidding behavior the same way risk aversion does, but the main result is that this is not the case for continuous price descending auctions. This is new among a few theoretical cases where ambiguity aversion does not reinforce the risk aversion implications. |
| Keywords: | Ambiguity;Auctions;Revenue Equivalence. |
| JEL: | D03 D44 D89 |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:kubcen:2012022&r=upt |
| By: | Ulrich Schmidt |
| Abstract: | This paper analyzes insurance demand under prospect theory in a simple model with two states of the world and fair insurance contracts. We argue that two different reference points are reasonable in this framework, state-dependent initial wealth or final wealth after buying full insurance. Applying the value function of Tversky and Kahneman (1992), we find that for both reference points subjects will either demand full insurance or no insurance at all. Moreover, this decision depends on the probability of the loss: the higher the probability of the loss, the higher is the propensity to take up insurance. This result can explain empirical evidence which has shown that people are unwilling to insure rare losses at subsidized premiums and at the same time take-up insurance for moderate risks at highly loaded premiums |
| Keywords: | insurance demand, prospect theory, flood insurance, diminishing sensitivity, loss, aversion |
| JEL: | D14 D81 G21 |
| Date: | 2012–03 |
| URL: | http://d.repec.org/n?u=RePEc:kie:kieliw:1764&r=upt |
| By: | Keita Owari (Faculty of Economics, University of Tokyo) |
| Abstract: | The existence of optimal strategy in robust utility maximization is addressed when the utility function is finite on the entire real line. A delicate problem in this case is to find a ggood definitionh of admissible strategies to obtain an optimizer. Under certain assumptions, especially a time-consistency property of the set ‚o of probabilities which describes the model uncertainty, we show that an optimal strategy is obtained in the class of those whose wealths are supermartingales under all local martingale measures having a finite generalized entropy with one of P ¸ ‚o. |
| Date: | 2011–10 |
| URL: | http://d.repec.org/n?u=RePEc:cfi:fseres:cf257&r=upt |
| By: | Lefort, Jean-Philippe; Dominiak, Adam |
| Abstract: | In this paper we show that unlike in Bayesian frameworks asymmetric information does matter and can explain differences in common knowledge decisions due to ambiguous character of agents' private information. Agents share a common-but-not-necessarily-additive prior beliefs represented by capacities. It is shown that, if each agent's information partition is made up of unambiguous events in the sense of Nehring (1999, Mat. Soc. Sci. 38, 197-213), then it is impossible that the agents disagree on their commonly known decisions, whatever these decisions are : whether posterior beliefs or conditional expectations. Conversely, an agreement on conditional expectations, but not on posterior beliefs, implies that agents' private information must consist of Nehring-unambiguous events. The results obtained allow to attribute the existence of a speculative trade to the presence of agents' diverse and ambiguous information. |
| Keywords: | capacities; Ambiguity; No-Trade Theorem; Choquet expected utility theory; unambiguous events; Agreement Theorem; common knowledge; asymmetric information; |
| JEL: | D81 D82 |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:ner:dauphi:urn:hdl:123456789/8575&r=upt |
| By: | Zubanov, N.V. |
| Abstract: | The application of the classical "linear" model of incentive pay to the case when the noise is multiplicative to effort generates two predictions for a given strength of incentives: 1) more risk-averse workers will put in less effort, and 2) setting a performance target will weaken the negative risk aversion--effort link. The data from a real-effort laboratory experiment involving 85 student participants support both these predictions. Implications of the model and empirical findings to the literature on, and practice of, personnel management are discussed. |
| Keywords: | risk aversion;incentive pay;performance targets |
| Date: | 2012–03–20 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:eureri:1765032031&r=upt |
| By: | Mohammad Majid Fouladgar Author_Email: (Fateh Research Group, Tehran, Iran); Abdolreza Yadani-Chamzini (Fateh Research Group, Tehran, Iran); Mohammad Hossein Basiri (Tarbiat Modares University) |
| Keywords: | Decision Making, Fuzzy Set, Risk Management, Tunnelling |
| JEL: | M0 |
| Date: | 2011–06 |
| URL: | http://d.repec.org/n?u=RePEc:cms:1icm11:2011-087-331&r=upt |