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on Utility Models and Prospect Theory |
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Issue of 2021‒08‒09
fourteen papers chosen by |
| By: | Romain Gauchon (ISFA - Institut de Science Financière et d'Assurances); Karim Barigou (ISFA - Institut de Science Financière et d'Assurances) |
| Abstract: | Expected utility is an influential theory to study rational choice among risky assets. For each investment, an economic agent expects to receive a random payoff and therefore maximizes its expected utility. To the best of our knowledge, there exists no general procedure to take the derivative of the expected utility as a function of the investment without heavy assumptions on the underlying processes. This article considers expected utility maximization when payoffs are modeled by a family of random variables increasing with investment for the convolution order such as Poisson, Gamma or Exponential distributions. For several common utility functions, with the help of fractional calculus, we manage to obtain closed-form formulas for the expected utility derivative. The paper also provides two economic applications: production of competitive firms and investment in prevention. |
| Keywords: | Convolution order,Expected utility,Fractional calculus,Prevention |
| Date: | 2021–07–22 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-03295594&r= |
| By: | Isa, Berk Orkun; Yucel, Mustafa Eray |
| Abstract: | This paper lays down a mathematical model of political participation where participatory behavior functions as insurance against redistribution of resources. Abstracting a broad notion of political participation to its tangible bene�fits and costs, we elaborate the participatory behavior from the perspectives of Expected Utility and Cumulative Prospect Theory. Our elaboration reveals that the relative degrees of risk aversion and loss aversion yield a multiplicity of equilibria, sheds light on the recently observed absenteeism in political participation and suggest that participation would not increase unless the material domain of politics itself is altered. |
| Keywords: | Political Participation; Cumulative Prospect Theory; Risk Aversion; Insurance; Lobbying |
| JEL: | D72 P16 |
| Date: | 2020–07–05 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:108818&r= |
| By: | Marc Fleurbaey (PSE - Paris School of Economics - ENPC - École des Ponts ParisTech - ENS Paris - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique - EHESS - École des hautes études en sciences sociales - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, CNRS - Centre National de la Recherche Scientifique); Stéphane Zuber (PSE - Paris School of Economics - ENPC - École des Ponts ParisTech - ENS Paris - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique - EHESS - École des hautes études en sciences sociales - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, CNRS - Centre National de la Recherche Scientifique, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique) |
| Abstract: | How to evaluate and compare social prospects when there may be a risk on i) the actual allocation people will receive; ii) the existence of these future people; and iii) their preferences? This paper investigate this question that may arise when considering policies that endogenously affect future people, for instance climate policy. We show that there is no social ordering that meets minimal requirements of fairness, social rationality, and respect for people's ex ante preferences. We explore three ways to avoid this impossibility. First, if we drop the ex ante Pareto requirement, we can obtain fair ex post criteria that take an (arbitrary) expected utility of an equally-distributed equivalent level of well-being. Second, if the social ordering is not an expected utility, we can obtain fair ex ante criteria that assess uncertain individual prospects with a certainty-equivalent measure of well-being. Third, if we accept that interpersonal comparisons rely on VNM utility functions even in absence of risk, we can construct expected utility social orderings that satisfy of some version of Pareto ex ante. |
| Keywords: | Fairness,social risk,intergenerational equity |
| Date: | 2021–06 |
| URL: | http://d.repec.org/n?u=RePEc:hal:cesptp:halshs-03289160&r= |
| By: | Vincent Meisner; Jonas von Wangenheim |
| Abstract: | Evidence suggests that participants in direct student-proposing deferred-acceptance mechanisms (DSPDA) play dominated strategies. To explain the observed data, we introduce expectation-based loss aversion into a school-choice setting and characterize choice-acclimating personal equilibria in DSPDA. We find that non-truthful preference submissions can be strictly optimal if and only if they are top-choice monotone. In equilibrium, DSPDA may implement allocations with justified envy. Specifically, it discriminates against students who are more loss averse or less con- fident than their peers, and amplifies already existing discrimination. To level the playing field, we propose sequential mechanisms as an alternative that is robust to these biases. |
| Keywords: | Market design, Matching, School choice, Reference-dependent preferences, Loss aversion, Deferred acceptance |
| JEL: | C78 D47 D78 D81 D82 D91 |
| Date: | 2021–07 |
| URL: | http://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2021_312&r= |
| By: | Jonas von Wangenheim |
| Abstract: | Evidence suggests that people evaluate outcomes relative to expectations. I analyze this expectations-based loss aversion à la Köszegi and Rabin in the context of dynamic and static auctions, where the reference point is given by the (endogenous) equilibrium outcome. If agents update their reference point during the auction, the arrival of information crucially affects equilibrium behavior. Consequently, I show that - even with independent private values - the Vickrey auction yields strictly higher revenue than the (ascending clock) English auction, violating the well-known revenue equivalence. |
| Keywords: | Vickrey auction, English auction, Japanese auction, expectationsbased loss aversion, revenue equivalence, dynamic loss aversion, personal equilibrium |
| JEL: | D03 D44 |
| Date: | 2021–07 |
| URL: | http://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2021_313&r= |
| By: | Keisuke Kizaki (Graduate School of Economics, The University of Tokyo); Taiga Saito (Faculty of Economics, The University of Tokyo); Akihiko Takahashi (Faculty of Economics, The University of Tokyo) |
| Abstract: | This paper presents an equilibrium-based asset pricing model incorporating market sentiments, where multi-agents have heterogeneous (optimistic, pessimistic, neutral) views on fundamental risks represented by Brownian motions. Each agent maximizes its expected utility on consumption under its subjective probability measure, reflecting its heterogeneous views on fundamental risks. Specifically, we formulate the optimal consumption and portfolio problem with a choice of a probability measure. We investigate the probability measure, containing the sign of a volatility process for the expected utility in the probability density process, by a Malliavin calculus approach. Moreover, we provide an expression of the state- price density process that includes information on the interest rate and the market price of risk in equilibrium. Finally, we present a numerical example on pricing zero-coupon bonds, which shows the effects of the agents' heterogeneous views on the term structure of interest rates. |
| Date: | 2021–07 |
| URL: | http://d.repec.org/n?u=RePEc:tky:fseres:2021cf1173&r= |
| By: | Mira Frick (Cowles Foundation, Yale University); Ryota Iijima (Cowles Foundation, Yale University); Yves Le Yaouanq (Ludwig-Maximilians-Universit‰t, Munich) |
| Abstract: | We show how incorporating Gilboa, Maccheroni, Marinacci, and Schmeidler's (2010) notion of objective rationality into the alpha-MEU model of choice under ambiguity (Hurwicz, 1951) can overcome several challenges faced by the baseline model without objective rationality. The decision-maker (DM) has a subjectively rational preference $\succsim^\wedge$, which captures the complete ranking over acts the DM expresses when forced to make a choice; in addition, we endow the DM with a (possibly incomplete) objectively rational preference $\succsim^*$, which captures the rankings the DM deems uncontroversial. Under the objectively founded alpha-MEU model, $\succsim^\wedge$ has an alpha-MEU representation and $\succsim^*$ has a unanimity representation à la Bewley (2002), where both representations feature the same utility index and set of beliefs. While the axiomatic foundations of the baseline alpha-MEU model are still not fully understood, we provide a simple characterization of its objectively founded counterpart. Moreover, in contrast with the baseline model, the model parameters are uniquely identified. Finally, we provide axiomatic foundations for prior-by-prior Bayesian updating of the objectively founded alpha-MEU model, while we show that, for the baseline model, standard updating rules can be ill-defined. |
| Keywords: | Ambiguity, Alpha-MEU, Objective rationality, Updating |
| Date: | 2020–07 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:2244r&r= |
| By: | Tanaka, Yasuhito |
| Abstract: | In recent years, a school of economics called MMT (Modern Monetary Theory) has been attracting attention, but it has not been analyzed theoretically or mathematically. This study aims to provide a theoretical basis for the skeleton of the MMT argument, while maintaining the basics of the neoclassical microeconomic framework, such as utility maximization of consumers by means of utility functions and budget constraint, profit maximization of firms in monopolistic competition, and equilibrium of supply and demand of goods. Using a simple static model that includes economic growth due to technological progress, we will argue that: 1) a continuous budget deficit is necessary to maintain full employment when the economy is growing, and that this deficit does not have to be covered by future surpluses; 2) Inflation is caused when the actual budget deficit exceeds the level necessary and sufficient to maintain full employment. In order to avoid further inflation, it is necessary to maintain a certain level of budget deficit; 3) A shortfall in the budget deficit leads to recession and involuntary unemployment. To recover from this, a budget deficit that exceeds the level necessary to maintain full employment is required. However, since a continuous budget deficit is necessary after full employment is restored, the deficit created to overcome the recession does not need to be covered by future budget surpluses, nor should it be. |
| Keywords: | MMT, Economic growth, Budget deficit, Inflation |
| JEL: | E12 E24 |
| Date: | 2021–08–02 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:109005&r= |
| By: | Francesco Andreoli (Department of Economics, University of Verona, Italy and Luxembourg Institute of Socio-Economic Research, LISER); Mathieu Faure (Aix-Marseille Univ, CNRS, AMSE, Marseille, France.); Nicolas Gravel (Aix-Marseille Univ, CNRS, AMSE, Marseille, France.); Tista Kundu (Centre de Sciences Humaines, Delhi, India.) |
| Abstract: | This paper provides a robust criterion for evaluating the allocation of opportunities among various groups. We envisage the problem of comparing these allocations from the view point of an ethical observer placed behind a veil of ignorance with respect to the group in which he/she could end up. We give justi…cation for such an ethical observer to evaluate these allocations of opportunities on the basis of an expected valuation of the expected utility of being in a group assuming an equal probability of falling in every group. We identify a criterion for comparing societies that is agreed upon by all such ethical observers who exhibit aversion to inequality of opportunities. The criterion happens to be a conic extension of zonotope inclusion criterion. We provide various interpretations of this criterion as well as some illustrations of its possible use, notably in the Indian context where we evaluate the inequalities of educational opportunities among castes and genders o¤ered by Indian states. |
| Keywords: | equalizing opportunities, groups, zonotopes, gender, education |
| JEL: | D63 D81 I24 |
| Date: | 2021–07 |
| URL: | http://d.repec.org/n?u=RePEc:aim:wpaimx:2137&r= |
| By: | Grimaud, Alex |
| Abstract: | This paper revisits monetary policy in a heterogeneous agents new Keynesian (HANK) model where agents use adaptive learning (AL) in order to form their expectations. Due to the households' finite heterogeneity triggered by idiosyncratic unemployment risk, the model is subject to micro-founded heterogeneous expectations that are not anchored to the rational expectation path. Households experience different histories which has non-trivial consequences on their individual AL processes. In this model, supply shocks generate precautionary saving and possible long-lasting disinflationary traps associated with excess saving. Dovish policies focused on closing the output gap dampen the learning effects which is in contradiction with previously established representative agent under learning results. Price level targeting appears to resolve most of the problem by netter anchoring long-run expectations of future utility flows. |
| Keywords: | Adaptive learning, supply shocks, precautionary saving, heterogeneous expectations, HANK and price level targeting |
| JEL: | E25 E31 E52 |
| Date: | 2021–07–05 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:108931&r= |
| By: | Dean Spears (University of Texas at Austin [Austin], Indian Statistical Institute [New Delhi], IZA - Forschungsinstitut zur Zukunft der Arbeit - Institute of Labor Economics, IFFS - Institute for Futures Studies); Stéphane Zuber (PSE - Paris School of Economics - ENPC - École des Ponts ParisTech - ENS Paris - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique - EHESS - École des hautes études en sciences sociales - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, CNRS - Centre National de la Recherche Scientifique, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique) |
| Abstract: | Utilitarianism is the most prominent family of social welfare functions. We present three new axiomatic characterizations of utilitarian (that is, additively separable) social welfare functions in a setting where there is risk over both population size and the welfares of individuals. First, we show that, given uncontroversial basic axioms, Blackorby et al.'s (1998) Expected Critical-Level Generalized Utilitarianism (ECLGU) is equivalent to a new axiom holding that it is better to allocate higher utility-conditional-on-existence to possible people who have a higher probability of existence. The other two novel characterizations extend classic axiomatizations of utilitarianism from settings with either social risk or variable-population, considered alone. By considering both social risk and variable population together, we clarify the fundamental normative considerations underlying utilitarian policy evaluation. |
| Keywords: | Social risk,population ethics,utilitarianism,expected critical-level generalized utilitarianism,prioritarianism |
| Date: | 2021–05 |
| URL: | http://d.repec.org/n?u=RePEc:hal:cesptp:halshs-03287583&r= |
| By: | Ray C. Fair (Cowles Foundation, Yale University) |
| Abstract: | According to retrospective voting, a bad economy hurts the incumbent party and vice versa. According to risk-aversion voting as discussed in Pástor and Veronesi (2020), high risk aversion favors the Democrats over the Republicans and vice versa. If high risk aversion is associated with a bad economy, then risk-aversion voting implies that a bad economy favors the Democrats and vice versa. The two theories thus have different implications for the Democrats. This paper tests both theories under the assumption that high risk aversion is associated with a bad economy. The results provide no support for risk-aversion voting under this assumption. |
| Keywords: | Retrospective voting, Risk-aversion voting |
| JEL: | E00 |
| Date: | 2021–03 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:2279r&r= |
| By: | Benjamin Balzer; Antonio Rosato; Jonas von Wangenheim |
| Abstract: | We study Dutch and fi rst-price auctions with expectations-based loss-averse bidders and show that the strategic equivalence between these formats no longer holds. Intuitively, as the Dutch auction unfolds, a bidder becomes more optimistic about her chances of winning; this stronger "attachment" effect pushes her to bid more aggressively than in the first-price auction. Thus, Dutch auctions raise more revenue than first-price ones. Indeed, the Dutch auction raises the most revenue among standard auction formats. Our results imply that dynamic mechanisms that make bidders more optimistic raise more revenue, thereby ratio- nalizing the use of descending-price mechanisms by sellers in this field. |
| Keywords: | Loss Aversion, Dutch Auctions, Revenue Equivalence, Personal Equilibrium |
| JEL: | D44 D81 D82 |
| Date: | 2021–07 |
| URL: | http://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2021_314&r= |
| By: | Gérard Mondello (Université Côte d'Azur, France; GREDEG CNRS) |
| Abstract: | This paper studies the impact of the reliability of information sources on choices under ambiguity. Using the Ellsberg's (1961) framework it studies two conjectures. First, the conditions of appearance of the Ellsberg paradox when the information source offers two probable proportions of red and black balls in two urns. Second, the consequence on choices of a non-reliable information source. This source proposes a unique proportion of red and black balls against an unknown one (inside box 1). Thus, either the proportion is correct, or it is unknown (ambiguous). We show that despite le information source unreliability, the decision-maker will trust the given information. |
| Keywords: | Uncertainty theory, decision theory, ambiguity aversion, Information |
| JEL: | I10 I18 I19 D80 D81 D83 |
| Date: | 2021–07 |
| URL: | http://d.repec.org/n?u=RePEc:gre:wpaper:2021-31&r= |