
on Utility Models and Prospect Theory 
By:  David Dillenberger (University of Pennsylvania); Daniel Gottlieb (London School of Economics); Pietro Ortoleva (Princeton University) 
Abstract:  We study how the separation of time and risk preferences relates to a behavioral property that generalizes impatience to stochastic environments: Stochastic Impatience. We show that, within a broad class of models, Stochastic Impatience holds if and only if risk aversion is "not too high" relative to the inverse elasticity of intertemporal substitution. This result has implications for many known models. For example, for those of Epstein and Zin (1989) and Hansen and Sargent (1995), Stochastic Impatience is violated for all commonly used parameters. 
Keywords:  Stochastic Impatience, EpsteinZin preferences, Separation of Time and Risk preferences, Risk Sensitive preferences, NonExpected Utility 
JEL:  D81 D90 G11 E7 
Date:  2020–04 
URL:  http://d.repec.org/n?u=RePEc:pri:econom:202054&r= 
By:  Faruk R. Gul (Princeton University); Wolfgang Pesendorfer (Princeton University); Mu Zhang (Princeton University) 
Abstract:  We establish the existence of Walrasian equilibrium for economies with many discrete goods and possibly one divisible good. Our goal is not only to study Walrasian equilibria in new settings but also to facilitate the use of market mechanisms in resource allocation problems such as school choice or course selection. We consider all economies with quasilinear gross substitutes preferences but allow agents to have limited quantities of the divisible good (limited transfers economies). We also consider economies without adivisible good (nontransferable utility economies). We show the existence and efficiency of Walrasian equilibrium in limited transfers economies and the existence and efficiency of strong (Walrasian) equilibrium in nontransferable utility economies. Finally, we show that various constraints on minimum and maximum levels of consumption and aggregate constraints of the kind that are relevant for school choice/course selection problems can be accommodated by either incorporating these constraints into individual preferences or by incorporating a suitable production technology into nontransferable utility economies 
Keywords:  Walrasian equilibrium 
JEL:  D50 D59 
Date:  2020–06 
URL:  http://d.repec.org/n?u=RePEc:pri:econom:202038&r= 
By:  Ludovic Tangpi; Xuchen Zhou 
Abstract:  This paper studies a stochastic utility maximization game under relative performance concerns in finite agent and infinite agent settings, where a continuum of agents interact through a graphon (see definition below). We consider an incomplete market model in which agents have CARA utilities, and we obtain characterizations of Nash equilibria in both the finite agent and graphon paradigms. Under modest assumptions on the denseness of the interaction graph among the agents, we establish convergence results for the Nash equilibria and optimal utilities of the finite player problem to the infinite player problem. This result is achieved as an application of a general backward propagation of chaos type result for systems of interacting forwardbackward stochastic differential equations, where the interaction is heterogeneous and through the control processes, and the generator is of quadratic growth. In addition, characterizing the graphon game gives rise to a novel form of infinite dimensional forwardbackward stochastic differential equation of MckeanVlasov type, for which we provide wellposedness results. An interesting consequence of our result is the computation of the competition indifference capital, i.e., the capital making an investor indifferent between whether or not to compete. 
Date:  2022–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2202.11314&r= 
By:  Erhan Bayraktar; Tao Chen 
Abstract:  We consider a discrete time stochastic Markovian control problem under model uncertainty. Such uncertainty not only comes from the fact that the true probability law of the underlying stochastic process is unknown, but the parametric family of probability distributions which the true law belongs to is also unknown. We propose a nonparametric adaptive robust control methodology to deal with such problem. Our approach hinges on the following building concepts: first, using the adaptive robust paradigm to incorporate online learning and uncertainty reduction into the robust control problem; second, learning the unknown probability law through the empirical distribution, and representing uncertainty reduction in terms of a sequence of Wasserstein balls around the empirical distribution; third, using Lagrangian duality to convert the optimization over Wasserstein balls to a scalar optimization problem, and adopting a machine learning technique to achieve efficient computation of the optimal control. We illustrate our methodology by considering a utility maximization problem. Numerical comparisons show that the nonparametric adaptive robust control approach is preferable to the traditional robust frameworks. 
Date:  2022–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2202.10391&r= 
By:  Taiga Saito (Graduate School of Economics, The University of Tokyo); Akihiko Takahashi (Graduate School of Economics, The University of Tokyo) 
Abstract:  This paper considers a new problem for portfolio optimization with a choice of a probability measure, particularly optimal investment problem under sentiments. Firstly, we formulate the problem as a supsupinf problem consisting of optimal investment and a choice of a probability measure expressing aggressive and conservative attitudes of the investor. This problem also includes the case where the agent has conservative and neutral views on risks represented by Brownian motions and degrees of conservativeness differ among the risk. Secondly, we obtain an expression of the volatility process of a backward stochastic differential equation related to the conservative sentiment in order to investigate cases where the supsupinf problem is solved. Specifically, we take a Malliavin calculus approach to solve the problem and obtain an optimal portfolio process. Finally, we provide an expression of the optimal portfolio under the sentiments in two examples with stochastic uncertainties in an exponential utility case and investigate the impact of the sentiments on the portfolio process. 
Date:  2022–03 
URL:  http://d.repec.org/n?u=RePEc:cfi:fseres:cf534&r= 
By:  Vanessa MICHEL(OLTRA) 
Abstract:  Modern economic approaches of empathy and sympathy aim at adding an altruistic dimension to the standard economic decision theory. The purpose of the introduction of another regarding dimension, in addition to the sole personal interest, is to try to explain prosocial preferences or behaviours. In this article, we show how and why the economic literature tries to grasp those concepts, but in a way that is very far from the original Smithian sympathy developed in his Theory of Moral Sentiments (TSM). We argue that, by remaining in the framework of methodological individualism and instrumental rationality, economic approaches, particularly in the field of experimental and behavioural economics, tend to reduce and to intrumentalize the concepts of sympathy and empathy. Such approaches seem to us not consistent with the Smithian social philosophy of human nature and interpersonal relationships. 
Keywords:  Smithian sympathy, Empathy, Theory of moral snetiments, behavioural economics 
JEL:  B12 
Date:  2022 
URL:  http://d.repec.org/n?u=RePEc:grt:bdxewp:202203&r= 
By:  Andrei Savochkin (New Economic School); Alexander Shklyaev (Moscow State University); Alexey Galatenko (Moscow State University) 
Abstract:  We study the Smooth Ambiguity decision criterion in the dynamic setting to understand when it can satisfy the Dynamic Consistency and Consequentialism properties. Our result characterizes the possibility to have these properties through a condition that has the spirit of the rectangularity condition introduced by Epstein and Schneider (2003) for the maxmin model. Rectangularity enables specifying preferences recursively and solving applied models by Dynamic Programming. At the same time, we show that Dynamic Consistency and Consequentialism can be achieved for Smooth Ambiguity preferences in a narrower set of scenarios than one could expect. 
Keywords:  smooth ambiguity, dynamic consistency, rectangularity JEL Classifications: D81 
Date:  2022–03 
URL:  http://d.repec.org/n?u=RePEc:abo:neswpt:w0288&r= 
By:  Mickael Beaud (CEEM  Centre d'Economie de l'Environnement  Montpellier  UMR 5211  UM  Université de Montpellier  CNRS  Centre National de la Recherche Scientifique  Montpellier SupAgro  Institut national d’études supérieures agronomiques de Montpellier  INRAE  Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); Mathieu Lefebvre (AMSE  AixMarseille Sciences Economiques  EHESS  École des hautes études en sciences sociales  AMU  Aix Marseille Université  ECM  École Centrale de Marseille  CNRS  Centre National de la Recherche Scientifique); Julie Rosaz (CEREN  Centre de Recherche sur l'ENtreprise [Dijon]  BSB  Burgundy School of Business (BSB)  Ecole Supérieure de Commerce de Dijon Bourgogne (ESC)) 
Abstract:  We investigate whether and how an individual giving decision is affected in risky environments in which the recipient's wealth is random. We demonstrate that, under risk neutrality, the donation of dictators with a purely ex post view of fairness should, in general, be affected by the riskiness of the recipient's payoff, while dictators with a purely ex ante view should not be. Furthermore, we observe that some influential inequality aversion preferences functions yield opposite predictions when we consider ex post view of fairness. Hence, we report on dictator games laboratory experiments in which the recipient's wealth is exposed to an actuarially neutral and additive background risk. Our experimental data show no statistically significant impact of the recipient's risk exposure on dictators' giving decisions. This result appears robust to both the experimental design (within subjects or between subjects) and the origin of the recipient's risk exposure (chosen by the recipient or imposed on the recipient). Although we cannot sharply validate or invalidate alternative fairness theories, the whole pattern of our experimental data can be simply explained by assuming ex ante view of fairness and risk neutrality. 
Keywords:  Laboratory experiments,Dictator games,Background risk 
Date:  2022 
URL:  http://d.repec.org/n?u=RePEc:hal:journl:hal03559598&r= 
By:  Derek Messacar 
Abstract:  Using administrative data from Canada linked to a financial capability survey, I show that taxdeductible savings plans are often used to manipulate final balances owed to the central tax authority during tax season. This finding implies a strong avoidance motive for saving, where tax filers manipulate final balances rather than total tax liabilities, consistent with lossaversion. The magnitude of this effect is economically significant. For example, each $100 owed increases the likelihood of contributing by about half a percentage point. There is evidence that the behavior is driven by tax filers with low financial literacy who make disproportionately large contributions in the last 60 days before the annual deadline. 
Keywords:  Lossaversion, tax avoidance, savings, regression kink design 
JEL:  D14 D91 H26 H31 
Date:  2022 
URL:  http://d.repec.org/n?u=RePEc:rsi:irersi:8&r= 
By:  Benjamin Bruder; Nazar Kostyuchyk; Thierry Roncalli 
Abstract:  This article develops a model that takes into account skewness risk in risk parity portfolios. In this framework, asset returns are viewed as stochastic processes with jumps or random variables generated by a Gaussian mixture distribution. This dual representation allows us to show that skewness and jump risks are equivalent. As the mixture representation is simple, we obtain analytical formulas for computing asset risk contributions of a given portfolio. Therefore, we define risk budgeting portfolios and derive existence and uniqueness conditions. We then apply our model to the equity/bond/volatility asset mix policy. When assets exhibit jump risks like the short volatility strategy, we show that skewnessbased risk parity portfolios produce better allocation than volatilitybased risk parity portfolios. Finally, we illustrate how this model is suitable to manage the skewness risk of longonly equity factor portfolios and to allocate between alternative risk premia. 
Date:  2022–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2202.10721&r= 
By:  Koichi Futagami (Department of Economics, Doshisha University); Daiki Maeda (School of Global Studies, Chukyo University) 
Abstract:  We incorporate naive agents with a nonunitary discounting rate into a cash inadvance (CIA) model. Through this extension, we obtain the following results. First, we show that there exists an equilibrium in which the CIA constraint does not bind when individuals discount their utilities from future consumption lower than their utilities from future leisure time. It is important to note that this non binding equilibrium exists even if the nominal interest rate takes a positive value. Second, we demonstrate that increases in the money supply growth rate decreases the individuals f saving rate in the equilibrium in which the CIA constraint does not bind. Third, we exhibit that when the equilibrium where the CIA constraint does not bind exists, the welfare level of this equilibrium can be higher than that of the equilibrium in which the CIA constraint binds. Moreover, we deduce that the Friedman rule cannot be optimal in the equilibrium in which the CIA constraint binds and present the result that the optimal level of the optimal nominal interest rate is a?ected by the di?erence of the discount rates. 
Keywords:  Nonunitary discounting rate; Naive agents; CIA constraint; Monetary policy; Friedman rule 
JEL:  E52 E70 
URL:  http://d.repec.org/n?u=RePEc:osk:wpaper:2128&r= 