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on Utility Models and Prospect Theory |
| By: | Xu, Guo; Wing-Keung, Wong; Lixing, Zhu |
| Abstract: | In this paper we �first develop a theory of almost stochastic dominance for risk-seeking investors to the first three orders. Thereafter, we study the relationship between the preferences of almost stochastic dominance for risk-seekers with that for risk averters. |
| Keywords: | Almost Stochastic Dominance, expected-utility maximization, risk averters, risk seekers. |
| JEL: | C00 D81 G11 |
| Date: | 2013–11–27 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:51744&r=upt |
| By: | Nina, Boyarchenko; Mario, Cerrato; John, Crosby; Stewart, Hodges |
| Abstract: | Faced with the problem of pricing complex contingent claims, an investor seeks to make his valuations robust to model uncertainty. We construct a notion of a model- uncertainty-induced utility function and show that model uncertainty increases the investor's eff ective risk aversion. Using the model-uncertainty-induced utility function, we extend the \No Good Deals" methodology of Cochrane and Sa a-Requejo [2000] to compute lower and upper good deal bounds in the presence of model uncertainty. We illustrate the methodology using some numerical examples. |
| Keywords: | Asset pricing theory, Good deal bounds, Knightian uncertainty, Model uncertainty, Contingent claim pricing, model-uncertainty-induced utility function, |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:edn:sirdps:452&r=upt |
| By: | Ola Andersson (Research Institute of Industrial Economics (IFN)); Håkan J. Holm (Lund University - Department of Economics); Jean-Robert Tyran (Centre for Economic Policy Research (CEPR), University of Vienna, Department of Economics, Copenhagen University); Erik Wengström (Department of Economics, Copenhagen University) |
| Abstract: | Recent experimental studies suggest that risk aversion is negatively related to cognitive ability. In this paper we report evidence that this relation might be spurious. We recruit a large subject pool drawn from the general Danish population for our experiment. By presenting subjects with choice tasks that vary the bias induced by random choices, we are able to generate both negative and positive correlations between risk aversion and cognitive ability. Structural estimation allowing for heterogeneity of noise yields no significant relation between risk aversion and cognitive ability. Our results suggest that cognitive ability is related to random decision making rather than to risk preferences. |
| Keywords: | risk preference, cognitive ability, experiment, noise |
| JEL: | C81 C91 D12 D81 |
| Date: | 2013–09–04 |
| URL: | http://d.repec.org/n?u=RePEc:kud:kuiedp:1310&r=upt |
| By: | Manzini, Paola; Mariotti, Marco |
| Abstract: | We model the choice behaviour of an agent who suffers from imperfect attention but is otherwise von Neumann Morgenstern rational. We define inattention axiomatically through preference over menus and endowed alternatives: an agent is inattentive if it is better to be endowed with an alternative a than to be allowed to pick a from a menu in which a is is the best alternative. This property and vNM rationality on the domain of menus and alternatives imply that the agent notices each alternative with a given menu-dependent probability (attention parameter) and maximises a menu independent utility function over the alternatives he notices. Preference for flexibility restricts the model to menu independent attention parameters as in Manzini and Mariotti [17]. Our theory explains anomalies (e.g. the attraction effect) that other prominent stochastic choice theories cannot accommodate. |
| Keywords: | bounded rationality, stochastic choicens, |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:edn:sirdps:523&r=upt |
| By: | Ola Andersson (Research Institute of Industrial Economics (IFN)); Håkan J. Holm (Lund University - Department of Economics); Jean-Robert Tyran (Centre for Economic Policy Research (CEPR), University of Vienna, Department of Economics, Copenhagen University); Erik Wengström (Department of Economics, Copenhagen University) |
| Abstract: | We study risk taking on behalf of others,both with and without potential losses. A large-scale incentivized experiment is conducted with subjects randomly drawn from the Danish population. On average, decision makers take the same risks for other people as for themselves when losses are excluded. In contrast, when losses are possible, decisions on behalf of others are more risky. Using structural estimation, we show that this increase in risk stems from a decrease in loss aversion when others are affected by their choices. |
| Keywords: | risk taking, loss aversion, experiment |
| JEL: | C91 D03 D81 G02 |
| Date: | 2013–09–04 |
| URL: | http://d.repec.org/n?u=RePEc:kud:kuiedp:1309&r=upt |
| By: | Paola, Manzini; Marco, Mariotti |
| Abstract: | We model a boundedly rational agent who suffers from limited attention. The agent considers each feasible alternative with a given (unobservable) probability, the attention parameter, and then chooses the alternative that maximises a preference relation within the set of considered alternatives. We show that this random choice rule is the only one for which the impact of removing an alternative on the choice probability of any other alternative is asymmetric and menu independent. Both the preference relation and the attention parameters are identi fied uniquely by stochastic choice data. |
| Keywords: | Discrete choice, Random utility, Logit model, Luce model, Consideration sets, bounded rationality, revealed preferences, |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:edn:sirdps:463&r=upt |
| By: | Larry Epstein; Emmanuel Farhi; Tomasz Stralezcki |
| Abstract: | Though risk aversion and the elasticity of intertemporal substitution have been the subjects of careful scrutiny when calibrating preferences, the long-run risks literature as well as the broader literature using recursive utility to address asset pricing puzzles have ignored the full implications of their parameter specifications. Recursive utility implies that the temporal resolution of risk matters and a quantitative assessment of how much it matters should be part of the calibration process. This paper gives a sense of the magnitudes of implied timing premia. Its objective is to inject temporal resolution of risk into the discussion of the quantitative properties of long-run risks and related models. |
| Date: | 2013–01 |
| URL: | http://d.repec.org/n?u=RePEc:qsh:wpaper:136671&r=upt |
| By: | Alcantud, José Carlos R.; Bosi, Gianni; Zuanon, Magalì |
| Abstract: | We introduce a new kind of representation of a not necessarily total preorder, called strong multi-utility representation, according to which not only the preorder itself but also its strict part is fully represented by a family of multi-objective functions. The representability by means of semicontinuous or continuous multi-objective functions is discussed, as well as the relation between the existence of a strong multi-utility representation and the existence of a Richter-Peleg utility function. We further present conditions for the existence of a semicontinuous or continuous countable strong multi-utility representation. |
| Keywords: | Multi-utility representation, Richter-Peleg utility, Strong multi-utility |
| JEL: | C0 D01 |
| Date: | 2013–12–01 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:52329&r=upt |
| By: | Georgios, Gerasimou |
| Abstract: | This paper proposes a model of choice that does not assume completeness of the decision maker’s preferences. The model explains in a natural way, and within a unified framework of choice when preference-incomparable options are present, four behavioural phenomena: the attraction effect, choice deferral, the strengthening of the attraction effect when deferral is per-missible, and status quo bias. The key element in the proposed decision rule is that an individual chooses an alternative from a menu if it is worse than no other alternative in that menu and is also better than at least one. Utility-maximising behaviour is included as a special case when preferences are complete. The relevance of the partial dominance idea underlying the proposed choice procedure is illustrated with an intuitive generalisation of weakly dominated strategies and their iterated deletion in games with vector payoffs. |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:edn:sirdps:460&r=upt |
| By: | Dorian Jullien (University of Nice Sophia Antipolis; GREDEG CNRS) |
| Abstract: | This paper discusses the ways by which a certain type of behavioral deviation from expected utility theory has been handled by psychologists and economists. With respect to the historical background of decision theory in economics, it is argued that there are good reasons for more theoretical developments from this behavioral deviation. |
| Keywords: | behavioral economics, psychology, decision theory, microeconomics, rationality |
| JEL: | D00 D01 D03 B21 B41 |
| Date: | 2013–12 |
| URL: | http://d.repec.org/n?u=RePEc:gre:wpaper:2013-47&r=upt |
| By: | Ali al-Nowaihi; Sanjit Dhami |
| Abstract: | We consider a discounted utility model that has two components. (1) The instan- taneous utility is of the prospect theory form, thus, allowing for reference dependent outcomes. (2) The discount function embodies a ‘reference time’ to which all future outcomes are discounted back to, hence, the name, reference time theory. We allow the discount function to exhibit declining impatience, as in hyperbolic discounting models, subadditivity or both. We show that if the discount function is non-additive, then the presence of a reference time has important effects on intertemporal choices. For instance, this helps to explain apparently intransitive choices over time. We also show how several recent approaches to time discounting can be incorporated within our proposed framework; these include attribute models and models of uncertainty. |
| Keywords: | Discounted utility models; Reference time theory; Prospect theory; Hyperbolic discounting, Subadditive discounting. |
| JEL: | C60 D91 |
| Date: | 2013–11 |
| URL: | http://d.repec.org/n?u=RePEc:lec:leecon:13/26&r=upt |
| By: | Broll, Udo; Ergozue, Martin; Welzel, Peter; Wong, Wing-Keung |
| Abstract: | We study the optimal production of a competitive risk-averse firm under price uncertainty. We suppose that the firm is also regret-averse. For example, if market prices ex post turn out to be very high the firm might regret not producing more. If it turns out that the price is low the firm might regret an over-production. We find that optimal output under regret aversion might be higher than under risk aversion. We also prove that optimal production could increase or decrease when the regret-averse coefficient increases. In general, we show that the regret-avers firm tend to hedge their bets, taking into account the possibility that their decisions may turn out to be ex post not optimal. These predictions can help explain the fact the price uncertainty has not such an extreme impact than those would be derived from pure risk-averse preferences. |
| Keywords: | Firm, decision making, price uncertainty, regret aversion, risk aversion |
| JEL: | C02 G11 |
| Date: | 2013–11–25 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:51703&r=upt |
| By: | Diasakos, Theodoros M |
| Abstract: | I develop a model of endogenous bounded rationality due to search costs, arising implicitly from the problems complexity. The decision maker is not required to know the entire structure of the problem when making choices but can think ahead, through costly search, to reveal more of it. However, the costs of search are not assumed exogenously; they are inferred from revealed preferences through her choices. Thus, bounded rationality and its extent emerge endogenously: as problems become simpler or as the benefits of deeper search become larger relative to its costs, the choices more closely resemble those of a rational agent. For a fixed decision problem, the costs of search will vary across agents. For a given decision maker, they will vary across problems. The model explains, therefore, why the disparity, between observed choices and those prescribed under rationality, varies across agents and problems. It also suggests, under reasonable assumptions, an identifying prediction: a relation between the benefits of deeper search and the depth of the search. As long as calibration of the search costs is possible, this can be tested on any agent-problem pair. My approach provides a common framework for depicting the underlying limitations that force departures from rationality in different and unrelated decision-making situations. Specifically, I show that it is consistent with violations of timing independence in temporal framing problems, dynamic inconsistency and diversification bias in sequential versus simultaneous choice problems, and with plausible but contrasting risk attitudes across small- and large-stakes gambles. |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:edn:sirdps:510&r=upt |
| By: | Mongin, Philippe |
| Abstract: | De tous les problèmes conçus par la théorie de la décision, le paradoxe d'Allais est peut-être celui qui aura suscité l'intérêt le plus persistant. La théorie y a consacré assez de travaux techniques remarquables pour qu'il soit désormais possible à l'histoire et à la philosophie des sciences de l'examiner réflexivement. Dans sa partie historique, l'article restitue le contexte d'apparition du paradoxe - le colloque de Paris, en 1952, auquel assistaient les principaux théoriciens de la décision du moment. L'axiomatique de von Neumann et Morgenstern en 1947 leur avait donné des raisons nouvelles d'approuver l'hypothèse de l'utilité attendue, et le contre-exemple d'Allais visait précisément à ébranler leur conviction. Les questions de la controverse étaient de type normatif, mais elles se perdirent quand le "paradoxe d'Allais" gagna tardivement la célébrité dans des travaux des années 1980 qui le traitaient comme une simple réfutation empirique. Ils en firent l'enjeu de "théories de l'utilité non-espérée" qu'ils développaient de même sous le seul angle empirique. Dans sa partie philosophique, l'article cherche à évaluer ce déplacement d'interprétation. D'un certain côté, les théoriciens de la décision firent bien de libérer leur travail expérimental des complications du normatif, car ils parvinrent ainsi à des résultats éclairants : l'hypothèse de l'utilité espérée était empiriquement réfutée, la responsabilité principale en revenait à l'axiome d'indépendance de von Neumann-Morgenstern, et l'étape suivante était de transformer adéquatement cet axiome. D'un autre côté, ils eurent tort de négliger un trait fondamental de leur domaine : les comportements observés ne sont informatifs que si les agents sont prêts à les assumer de manière réfléchie, c'est-à-dire à leur prêter une certaine valeur normative. D'après la reconstruction proposée ici, Allais ne voulait faire porter les expériences de choix que sur des sujets rationnels, ou bien sélectionnés au départ, ou bien révélés comme tels par l'expérience. L'article développe ces intuitions en revenant aux travaux des années 1970, aujourd'hui très peu connus, qui, sous l'influence d'Allais, proposèrent des traductions expérimentales de la rationalité, et il invite finalement la théorie de la décision à diversifier ses méthodes en s'inspirant de ces tentatives originales. Few problems in decision theory have raised more persisting interest than the Allais paradox. It appears that sufficiently many brilliant works have addressed it from within decision theory proper for history and philosophy of science now to enter stage. In its historical side, the paper recounts the paradox as it arose, i.e., in 1952, at a Paris conference attended by the main decision theorists of the time. They had drawn renewed confidence in expected utility theory (EUT) from the way von Neumann and Morgenstern had axiomatized it in 1947, and Allais devised his puzzle precisely to shaken their confidence. The issues between the two camps were normative, but they became lost in the developments of the 1980s that belatedly brought fame to the "Allais paradox". These works restricted the paradox to be a straightforward empirical refutation, turning it into a stake of also exclusively empirically oriented non-EU theories. In its philosophical vein, the paper tries to evaluate this shift of interpretation. To an extent, decision theorists were right because their experimental work was thus freed from a major complication and amenable to illuminating results: EUT was empirically refuted, the independence axiom of von Neumann and Morgentern was the main culprit, and the next theoretical stage was to modify this axiom appropriately. However, they were also wrong in not addressing an essential feature of their field, i.e., that observed behaviour is informative only if agents are prepared to endorse it reflectingly, i.e., to endow it with some normative value. As reconstructed here, Allais meant to reserve choice experiments to rational subjects, who were either selected at the outset, or identified as such by the experimental results. The paper tries to flesh out Allais's intuitions by turning to by now little known works of the 1970s, which under his influence provided experimental renderings of rationality, and it eventually suggests that decision theory might diversify its methods by taking inspiration from these original attempts. |
| Keywords: | Allais Paradox; expected utility theory; von Neumann-Morgenstern; positive vs normative; experimental economics of decision; rationality |
| JEL: | B21 B31 B41 C91 D81 |
| Date: | 2013–06–30 |
| URL: | http://d.repec.org/n?u=RePEc:ebg:heccah:1021&r=upt |
| By: | Guo, Xu; Post, Thierry; Wong, Wing-Keung; Zhu, Lixing |
| Abstract: | This study establishes necessary conditions for Almost Stochastic Dominance criteria of various orders. These conditions take the form of restrictions on algebraic combinations of moments of the probability distributions in question. The relevant set of conditions depends on the relevant order of ASD but not on the critical value for the admissible violation area. These conditions can help to reduce the information requirement and computational burden in practical applications. A numerical example and an empirical application to historical stock market data illustrate the moment conditions. The first four moment conditions in particular seem appealing for many applications. |
| Keywords: | decision theory; utility theory; stochastic dominance; necessary conditions; moments. |
| JEL: | C00 D81 G11 |
| Date: | 2013–11–26 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:51725&r=upt |
| By: | Ali al-Nowaihi; Sanjit Dhami |
| Abstract: | A critical element in all discounted utility models is the specification of a discount function. We extend the standard model to allow for reference points for both out- comes and time. We consider the axiomatic foundations and properties of two main classes of discount functions. The first, the Loewenstein-Prelec discount function, accounts for declining impatience but cannot account for the evidence on subadditivity. A second class of discount functions, the Read-Scholten discount function accounts for declining impatience and subadditivity. We derive restrictions on an individual’s preferences to expedite or to delay an outcome that give rise to the discount functions under consideration. As an application of our framework we consider the explanation of the common difference effect. |
| Keywords: | Hyperbolic discounting, Subadditive and superadditive discounting; Prospect theory, |
| JEL: | C60 D91 |
| Date: | 2013–11 |
| URL: | http://d.repec.org/n?u=RePEc:lec:leecon:13/27&r=upt |
| By: | CHINY, FAYCAL |
| Abstract: | In a world characterized by the occurrence of uncontrollable and extreme events investors are often required to make decisions on the basis of the available information. The challenge they face is how to manipulate these information sets in order to get what can lead them to the optimal decision. This logical way of thinking allows us to face two major ideas. The first idea is that each one of us has his own way to see the world and his own utility function that he will try to maximize. The second is where each one seeking to maximize his utility function is intuitively constrained to minimize the risk. The means that can combine these two aims is a well-defined investment process. Through this paper work we tried to summarize around 26 years of experience of a group of traders and investment advisors. What’s common to all of them is the definition of some standardized rules that must be followed but each one can adapt them to his proper needs and preferences. |
| Keywords: | Process, Investment, risk, utility function |
| JEL: | D81 D83 G11 G14 |
| Date: | 2013–12–27 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:52527&r=upt |
| By: | Giulia Di Nunno; Steffen Sjursen |
| Abstract: | We study optimal investment in an asset subject to risk of default for investors that rely on different levels of information. The price dynamics can include noises both from a Wiener process and a Poisson random measure with infinite activity. The default events are modelled via a counting process in line with large part of the literature in credit risk. In order to deal with both cases of inside and partial information we consider the framework of the anticipating calculus of forward integration. This does not require a priori assumptions typical of the framework of enlargement of filtrations. We find necessary and sufficient conditions for the existence of a locally maximizing portfolio of the expected utility at terminal time. We consider a large class of utility functions. In addition we show that the existence of the solution implies the semi-martingale property of the noises driving the stock. Some discussion on unicity of the maxima is included. |
| Date: | 2013–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1312.6032&r=upt |
| By: | Xu, Guo; Wing-Keung , Wong; Lixing, Zhu |
| Abstract: | This paper investigates the impact of background risk on an investor’s portfolio choice in a mean-VaR, mean-CVaR and mean-variance framework, and analyzes the characterizations of the mean-variance boundary and mean-VaR efficient frontier in the presence of background risk. We also consider the case with a risk-free security. |
| Keywords: | Background risk; Portfolio selection; VaR; CVaR |
| JEL: | C00 G11 |
| Date: | 2013–12–01 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:51827&r=upt |
| By: | Xiao Yu Wang |
| Abstract: | Mechanisms which implement stable matchings are often observed to work well in practice, even in environments where the stable outcome is not unique, information is complete, and the number of players is small. Why might individuals refrain from strategic manipulation, even when the complexity cost of manipulation is low? I study a two-sided, one-to-one matching problem with no side transfers, where utility is interdependent in the following intuitive sense: an individual's utility from a match depends not only on her preference ranking of her assigned partner, but also on that partner's ranking of her. I show that, in a world of complete information and linear interdependence, a unique stable matching emerges, and is attained by a modified Gale-Shapley deferred acceptance algorithm. As a result, a stable rule supports truth-telling as an equilibrium strategy. Hence, these results offer a new intuition for why stable matching mechanisms seem to work well in practice, despite their theoretic manipulability: individuals may value being liked. |
| Keywords: | two-sided matching, interdependent utility, stability |
| JEL: | C78 D82 |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:duk:dukeec:13-22&r=upt |
| By: | Dalton, Patricio S.; Ghosal, Sayantan |
| Abstract: | A number of different models with behavioral economics have a reduced form representation where potentially boundedly rational decision-makers do not necessarily internalize all the consequences of their actions on payoff relevant features (which we label as psychological states) of the choice environment. This paper studies the restrictions that such behavioral models impose on choice data and the implications they have for welfare analysis. First, we propose a welfare benchmark that is justified using standard axioms of rational choice and can be applied to a number of existing seminal behavioral economics models. Second, we show that Sen's axioms and fully characterize choice data consistent with behavioral decision-makers. Third, we show how choice data to infer information about the normative signi.cance of psychological states and establish the possibility of identifying welfare dominated choices. |
| Keywords: | Behavioral Choices, Revealed and Normative Preferences, Individual Welfare, Axiomatic Characterization, |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:edn:sirdps:503&r=upt |
| By: | Xiao Yu Wang |
| Abstract: | This note identifies a moral hazard environment in which a piecewise linear compensation scheme is optimal. Both the principal and the agent have CARA utility, mean output is increasing in the agent's non-contractible input, and output is distributed according to a Laplace distribution, which resembles a normal distribution (e.g. it is symmetric about the mean), but has fatter tails. The key property of the Laplace distribution is that the likelihood ratio is a piecewise constant, where the discontinuity occurs at the mean. The value of this approach is twofold: First, a tractable, empirically-observed wage scheme emerges as the equilibrium in a simple static contracting model. Second, the optimal piecewise linear scheme cleanly separates insurance and incentive provision. The linearity at output levels away from the mean captures insurance, while the jump at the mean captures incentive provision. Hence, this model is well-suited for studying a wide variety of principal-agent problems in risky environments subject to moral hazard, such as the effect of risk and moral hazard considerations on employment relationships in developing economies. |
| Keywords: | principal agent problems, moral hazard, linear incentive schemes, insurance, incentives |
| JEL: | C70 D86 O12 |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:duk:dukeec:13-23&r=upt |
| By: | Tejada, J.; Borm, P.E.M.; Lohmann, E.R.M.A. (Tilburg University, Center for Economic Research) |
| Abstract: | Abstract: We present a unifying framework for transferable utility coalitional games that are derived from a non-negative matrix in which every entry represents the value obtained by combining the corresponding row and column. We assume that every row and every column is associated with a player, and that every player is associated with at most one row and at most one column. The instances arising from this framework are called matching games, and they encompass assignment games and permutation games as two polar cases. We show that the core of a matching game is always nonempty by proving that the set of matching games coincides with the set of permutation games. Then we focus on two separate problems. First, we exploit the wide range of situations comprised in our framework to investigate the relationship between matching games with different player sets but defined by the same underlying matrix. We show that the core is not only immune to the merging of a row player and a column player, but also to the reverse manipulation, i.e., to the splitting of a player into a row player and a column player. Other common solution concepts fail to be either merging-proof or splitting-proof in general. Second, we focus on permutation games only and we analyze the set of all matrices that define permutation games with the same core. In contrast to assignment games, we show that there can be multiple matrices whose entries cannot be raised without modifying the core of the corresponding permutation game and that, for small instances, every such matrix defines an exact game. |
| Keywords: | matching situations;permutation games;assignment games |
| JEL: | C71 |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:kubcen:2013069&r=upt |