
on Utility Models and Prospect Theory 
Issue of 2022‒01‒24
fifteen papers chosen by 
By:  Jianming Xia 
Abstract:  A risk measure that is consistent with the secondorder stochastic dominance and additive for sums of independent random variables can be represented as a weighted entropic risk measure (WERM). The expected utility maximization problem with risk controlled by WERM and a related risk minimization problem are investigated in this paper. The latter is same to a problem of maximizing a weighted average of constantabsoluteriskaversion (CARA) certainty equivalents. The solutions of all the optimization problems are explicitly characterized and an iterative method of the solutions is provided. 
Date:  2021–12 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2112.02284&r= 
By:  Drugeon, JeanPierre; HaHuy, Thai 
Abstract:  This article completes an axiomatic approach of utilities streams. The approach is more precisely based upon the robust preorders that open the scope for $\alpha$MaxMin representations. A general $T$steps Temporal Bias axiom is first introduced, that encapsulates stationarity and $1$step present bias, aka quasihyperbolic discounting, as special cases. A detailed characterisation of the sets of probabilities that represent the weights of the future values of the utilities stream is then completed. This is first achieved for the close future preorder where a generalised picture of present biases in brought into evidence. This is complemented for the distant future preorder where it proved that, under the same system of axioms, the weights of the tail of the utility stream now correspond to Banach limits, who, in the evaluation of distant future, can be considered as the counterpart of the geometric discount rates in the evaluation of close future. The whole result is eventually given in an explicit $\alpha$Maxmin representation. 
Keywords:  Axiomatisation, Myopia, Multiple Discounts, $\alpha$MaxMin Citeria, Temporal Biases, Banach Limits, Infinite Dimensional Topologies. 
JEL:  D90 
Date:  2021–12–29 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:111306&r= 
By:  Zongxia Liang; Fengyi Yuan 
Abstract:  We provide a unified approach to find equilibrium solutions for timeinconsistent problems with distribution dependent rewards, which are important to the study of behavioral finance and economics. Our approach is based on {\it equilibrium master equation}, a nonlocal partial differential equation on Wasserstein space. We refine the classical notion of derivatives with respect to distribution, and establish It$\hato$'s formula in the sense of such refined derivatives. As applications, we reexamine the dynamic portfolio choice problem with rank dependent utility based the proposed novel approach. We also recover the celebrated extended HJB equation when reward of the problem has a nonlinear function of expectation, while reformulate and weaken the assumptions needed. Most importantly, we provide a protocol to find equilibrium solution of a dynamic meanES portfolio choice problem, which is completely new to the literature. 
Date:  2021–12 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2112.14462&r= 
By:  Emerson Melo 
Abstract:  This paper studies the Random Utility Model (RUM) in environments where the decision maker is imperfectly informed about the payoffs associated to each of the alternatives he faces. By embedding the RUM into an online decision problem, we make four contributions. First, we propose a gradientbased learning algorithm and show that a large class of RUMs are Hannan consistent (\citet{Hahn1957}); that is, the average difference between the expected payoffs generated by a RUM and that of the best fixed policy in hindsight goes to zero as the number of periods increase. Second, we show that the class of Generalized Extreme Value (GEV) models can be implemented with our learning algorithm. Examples in the GEV class include the Nested Logit, Ordered, and Product Differentiation models among many others. Third, we show that our gradientbased algorithm is the dual, in a convex analysis sense, of the Follow the Regularized Leader (FTRL) algorithm, which is widely used in the Machine Learning literature. Finally, we discuss how our approach can incorporate recency bias and be used to implement prediction markets in general environments. 
Date:  2021–12 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2112.10993&r= 
By:  Hernán Bejarano (CIDE / ESI Chapman University); Joris Gillet (Middlesex University London); Ismael RodriguezLara (Universidad de Granada) 
Abstract:  We study behavior in a trust game where firstmovers initially have a higher endowment than secondmovers but the occurrence of a positive random shock can eliminate this inequality by increasing the endowment of the secondmover before the decision of the firstmover. We find that secondmovers return less (i.e., they are less trustworthy) when they have a lower endowment than firstmovers, compared with the case in which first and secondmovers have the same endowment. Secondmovers who have experienced the positive shock return more than those who did not; in fact, secondmovers who have experienced the positive shock return more than secondmovers who had the same endowment as the firstmover from the outset. Firstmovers do not seem to anticipate this behavior from secondmovers. They send less to secondmovers who benefited from a shock. These findings suggest that in addition to the distribution of the endowments the source of this distribution plays an important role in determining the levels of trust and trustworthiness. This, in turn, implies that current models of inequality aversion should be extended to accommodate for reference points if random positive shocks are possible in the trust game. 
Keywords:  Trust game, endowment heterogeneity, random shocks, luck, inequality, aversion, referencedependent utility, reference points. 
JEL:  C91 D02 D03 D69 
Date:  2021–12 
URL:  http://d.repec.org/n?u=RePEc:aoz:wpaper:96&r= 
By:  Matthew Polisson; John Quah 
Abstract:  This note explains the equivalence between approximate rationalizability and ap proximate costrationalizability within the context of consumer demand. In connection with these results, we interpret Afriatâ€™s (1973) critical cost efficiency index (CCEI) as a measure of cost (in)efficiency, in the sense that a consumer is spending more money than is required to achieve her utility targets. 
Date:  2022–01–05 
URL:  http://d.repec.org/n?u=RePEc:bri:uobdis:22/754&r= 
By:  Benjamin Enke; Thomas Graeber 
Abstract:  This paper studies the relevance of cognitive uncertainty – subjective uncertainty over one's utilitymaximizing action – for understanding and predicting intertemporal choice. The main idea is that when people are cognitively noisy, such as when a decision is complex, they implicitly treat different time delays to some degree alike. By experimentally measuring and manipulating cognitive uncertainty, we document three economic implications of this idea. First, cognitive uncertainty explains various core empirical regularities, such as why people often appear very impatient, why perperiod impatience is smaller over long than over short horizons, why discounting is often hyperbolic even when the present is not involved, and why choices frequently violate transitivity. Second, impatience is contextdependent: discounting is substantially more hyperbolic when the decision environment is more complex. Third, cognitive uncertainty matters for choice architecture: people who are nervous about making mistakes are twice as likely to follow expert advice to be more patient. 
JEL:  D01 D03 
Date:  2021–12 
URL:  http://d.repec.org/n?u=RePEc:nbr:nberwo:29577&r= 
By:  Barigozzi, Francesca (University of Bologna); Cremer, Helmuth (Toulouse School of Economics) 
Abstract:  We study how workers' concern for coworkers' ability (CfCA) affects competition in the labor market. We consider two firms offering nonlinear contracts to a unit mass of prospective workers. Firms may differ in their marginal productivity, while workers are heterogeneous in their ability (high or low), and in their taste for being employed by any of the two firms. Workers receive a utility premium when employed by the firm hiring the workforce with larger average ability and they suffer a utility loss in the opposite case. These premiums/losses are endogenously determined. When workers' ability is observable and the difference in firms' marginal productivities is strictly positive, we show that CfCA increases surplus but it also increases firms' competition for highability workers. As a result, CfCA benefits highability workers but is detrimental to firms. In addition, CfCA exacerbates the existing distortion in sorting of highability workers to firms: too many workers are hired by the least efficient firm. When ability is not observable, the additional surplus appropriated by highability workers is eroded by overincentivization (countervailing incentives) and the more so when CfCA is high. Conversely, hightypes' sorting improves when CfCA is low and remains the same when it is high. 
Keywords:  screening, competition, concern for coworkersâ€™ quality, sorting 
JEL:  D82 L13 M54 
Date:  2021–11 
URL:  http://d.repec.org/n?u=RePEc:iza:izadps:dp14855&r= 
By:  Guilhem Lecouteux (UCA  Université Côte d'Azur, GREDEG  Groupe de Recherche en Droit, Economie et Gestion  UNS  Université Nice Sophia Antipolis (...  2019)  COMUE UCA  COMUE Université Côte d'Azur (2015  2019)  CNRS  Centre National de la Recherche Scientifique  UCA  Université Côte d'Azur) 
Abstract:  Behavioural economics has challenged the normative consensus that agents ought to choose following their own preferences. I argue that normative economists implicitly defended a criterion of the sovereignty of the autonomous consumer, and that current debates in normative behavioural economics arise from disagreements about the nature of the threats to autonomy that are highlighted by behavioural economics. I argue that those disagreements result from diverging ontological conceptions of the 'self' in the literature. I distinguish between the unitary, psychodynamic, and sociohistorical conceptions of the self, and show how different positive theories about preferences and the nature of the agent may determine normative positions in normative behavioural economics. 
Keywords:  preference satisfaction,autonomy,welfare,reconciliation problem,sociohistorical self 
Date:  2021 
URL:  http://d.repec.org/n?u=RePEc:hal:journl:halshs03418228&r= 
By:  Ms. Deniz O Igan; Antoine Levy; Mr. Taehoon Kim 
Abstract:  Statecontingent debt instruments such as GDPlinked warrants have garnered attention as a potential tool to help debtstressed economies smooth repayments over business cycles, yet very few studies of the empirical properties of these instruments exist. This paper develops a general f ramework to estimate the timevarying risk premium of a statecontingent sovereign debt instrument. Our estimation framework applied to GDPlinked warrants issued by Argentina, Greece, and Ukraine reveals three stylized facts: (i) the risk premium in statecontingent instruments is high and persistent; (ii) the risk premium exhibits a procyclical pattern; and (iii) the liquidity premium is higher and more volatile than that for plainvanilla government bonds issued by the same sovereign. We then present a model in which investors fear ambiguity and that can account for the cyclical properties of the risk premium. 
Keywords:  Statecontingent debt instruments; GDPlinked warrants; Risk premia; Procyclicality 
Date:  2021–12–03 
URL:  http://d.repec.org/n?u=RePEc:imf:imfwpa:2021/282&r= 
By:  Victor Filipe Martins da Rocha (LEDa  Laboratoire d'Economie de Dauphine  CNRS  Centre National de la Recherche Scientifique  IRD  Institut de Recherche pour le Développement  Université Paris DauphinePSL  PSL  Université Paris sciences et lettres, EESP  Sao Paulo School of Economics  FGV  Fundacao Getulio Vargas [Rio de Janeiro]); Rafael Mouallem Rosa (EESP  Sao Paulo School of Economics  FGV  Fundacao Getulio Vargas [Rio de Janeiro]) 
Abstract:  For an infinite horizon economy with complete contingent markets and bankruptcy risk, like the one studied by Araujo and Sandroni (1999) and Araujo, da Silva and Faro (2016), we show that an equilibrium may fail to exist even if agents' beliefs are homogeneous. In order to discourage agents from making promises that they know in advance they will not be able to keep, default penalties must be harsh enough. The minimum level of penalty compatible with equilibrium depends on the agents' distribution of beliefs and utility functions. When beliefs are asymptotically homogeneous, it is possible to find a uniform lower bound for the severity of the penalty. When beliefs are asymptotically singular, it is still possible to find default penalties compatible with equilibrium but they must be stochastic and unbounded in the long run. We also show how these positive results depend crucially on the interpretation of default penalties. In particular, if we consider explicit economic punishments, similar to those in Kehoe and Levine (1993), then an equilibrium never exists, even if agents' beliefs are homogeneous. 
Date:  2022 
URL:  http://d.repec.org/n?u=RePEc:hal:journl:hal02921220&r= 
By:  Drugeon, JeanPierre; HaHuy, Thai 
Abstract:  This study adresses timedependent orders that are shown to lead to recursive representations based upon a MaxMin dichotomy and introduce a structure that is naturally based upon timevarying multiple discounts. It is argued that this setup naturally provides an enriched understanding of the much discussed present biases. It is established how a multiple discounts version of \emph{present biais} becomes available and directly builds upon the features of the order defined from the head of the utilities sequence. 
Keywords:  Axiomatization, TimeDependent Orders, TimeVarying Multiple Discounts, Multiple Present Biases. 
JEL:  D9 D90 D91 
Date:  2021–12–29 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:111308&r= 
By:  Brown, David P. (University of Alberta, Department of Economics); Sappington, David E.M. (University of Florida) 
Abstract:  We examine the distinct impacts of forward contracting on generators and buyers of electricity. Increased forward contracting systematically reduces the variance of a generator's profit but can increase the variance of a buyer's profit. Consequently, increased risk aversion or market uncertainty can lead buyers, but not generators, to prefer reduced levels of forward contracting. We examine how the extent of equilibrium forward contracting varies with industry conditions, including the number of generators, the number of buyers, their aversion to profit variation, and the structure of retail electricity prices. 
Keywords:  forward contracting; risk aversion; electricity sector 
JEL:  L51 L94 Q28 Q40 
Date:  2021–12–31 
URL:  http://d.repec.org/n?u=RePEc:ris:albaec:2021_012&r= 
By:  Satoshi Nakada (School of Management, Department of Business Economics, Tokyo University of Science); Shmuel Nitzan (Department of Economics, BarIlan University); Takashi Ui (Department of Economics, Hitotsubashi University) 
Abstract:  This paper proposes normative criteria for voting rules under uncertainty about individual preferences to characterize a weighted majority rule (WMR). The criteria stress the significance of responsiveness, i.e., the probability that the social outcome coincides with the realized individual preferences. A voting rule is said to be robust if, for any probability distribution of preferences, the responsiveness of at least one individual is greater than onehalf. This condition is equivalent to the seemingly stronger condition requiring that, for any probability distribution of preferences and any deterministic voting rule, the responsiveness of at least one individual is greater than that under the deterministic voting rule. Our main result establishes that a voting rule is robust if and only if it is a WMR without ties. This characterization of a WMR avoiding the worst possible outcomes provides a new complement to the wellknown characterization of a WMR achieving the optimal outcomes, i.e., efficiency in the set of all random voting rules. 
Keywords:  majority rule, weighted majority rule, responsiveness, belieffree criterion. 
JEL:  D71 D81 
URL:  http://d.repec.org/n?u=RePEc:upd:utmpwp:038&r= 
By:  Qian Lei; Chi Seng Pun 
Abstract:  This paper proves the existence and uniqueness results (in the sense of maximally defined regularity) as well as the stability analysis for the solutions to a class of nonlocal fullynonlinear parabolic systems, where the nonlocality stems from the flow feature (controlled by an external temporal parameter) of the systems. The derived mathematical results generalize the theory of stochastic differential games to incorporate with behavioral factors such as timeinconsistent preferences, which facilitate developments of many studies in financial economics including robust stochastic controls and games under relative performance concerns. Moreover, with the wellposedness results, we establish a general multidimensional FeynmanKac formula in the presence of nonlocality (time inconsistency). 
Date:  2021–12 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2112.14409&r= 