
on Utility Models and Prospect Theory 
Issue of 2022‒11‒21
nine papers chosen by 
By:  Zongxia Liang; Guohui Guan; Yilun Song 
Abstract:  This paper studies the continuoustime precommitment KMM problem proposed by Klibanoff, Marinacci and Mukerji (2005) in incomplete financial markets, which concerns with the portfolio selection under smooth ambiguity. The decision maker (DM) is uncertain about the dominated priors of the financial market, which are characterized by a secondorder distribution (SOD). The KMM model separates risk attitudes and ambiguity attitudes apart and the aim of the DM is to maximize the twofold utility of terminal wealth, which does not belong to the classical subjective utility maximization problem. By constructing the efficient frontier, the original KMM problem is first simplified as an onefold expected utility problem on the secondorder space. In order to solve the equivalent simplified problem, this paper imposes an assumption and introduces a new distorted Legendre transformation to establish the bipolar relation and the distorted duality theorem. Then, under a further assumption that the asymptotic elasticity of the ambiguous attitude is less than 1, the uniqueness and existence of the solution to the KMM problem are shown and we obtain the semiexplicit forms of the optimal terminal wealth and the optimal strategy. Explicit forms of optimal strategies are presented for CRRA, CARA and HARA utilities in the case of Gaussian SOD in a BlackScholes financial market, which show that DM with higher ambiguity aversion tends to be more concerned about extreme market conditions with larger bias. In the end of this work, numerical comparisons with the DMs ignoring ambiguity are revealed to illustrate the effects of ambiguity on the optimal strategies and value functions. 
Date:  2022–10 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2210.13833&r=upt 
By:  Yuki SHIGETA 
Abstract:  This paper is concerned with the verification of a continuoustime utility max imization problem frequently used in recent macroeconomics. By focusing on Markov chain uncertainty, the problem in this paper can feature many charac teristics of a typical consumer’s problem in macroeconomics, such as borrowing constraints, endogenous labor supply, unhedgeable labor income, multiple asset choice, stochastic changes in preference, and others. I show that the value func tion of the problem is actually a constrained viscosity solution to the associated Hamilton–Jacobi–Bellman equation. Furthermore, the value function is continu ously differentiable in the interior of its domain. Finally, the candidate optimal control is admissible, unique, and actually optimal. 
Keywords:  ContinuousTime Utility Maximization, Borrowing Constraints, Hamilton–Jacobi–Bellman Equation, Viscosity Solution 
JEL:  C61 E21 G11 
Date:  2022–10 
URL:  http://d.repec.org/n?u=RePEc:kue:epaper:e22009&r=upt 
By:  Max Nendel 
Abstract:  In this paper, we show that the continuity from below of monotone functionals on $C_b$ is equivalent to their lower semicontinuity in the mixed topology. In the convex case, we obtain an alternative proof of a recent result by Freddy Delbaen for convex increasing functionals and monetary utility functions on the space of bounded continuous functions. 
Date:  2022–10 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2210.09133&r=upt 
By:  Patrice Loisel (MISTEA  Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie  INRA  Institut National de la Recherche Agronomique  Montpellier SupAgro  Institut national d’études supérieures agronomiques de Montpellier); Marielle Brunette (BETA  Bureau d'Économie Théorique et Appliquée  AgroParisTech  UNISTRA  Université de Strasbourg  UL  Université de Lorraine  CNRS  Centre National de la Recherche Scientifique  INRAE  Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); Stéphane Couture (MIAT INRAE  Unité de Mathématiques et Informatique Appliquées de Toulouse  INRAE  Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement) 
Abstract:  Storm is a major risk in forestry. However, due to the more or less pessimistic scenarios of future climate change, storm frequency is now ambiguous and only partially known (i.e., scenario ambiguity). Furthermore, within each scenario, the quantification of storm frequency is also ambiguous due to the differences in risk quantification by experts, creating a second level of ambiguity (i.e., frequency ambiguity). In such an ambiguous context, knowledge of the future climate through accurate information about this risk is fundamental and can be of significant value. In this paper, we question how ambiguity and ambiguity aversion affect forest management, in particular, optimal cutting age. Using a classical Faustmann framework of forest rotation decisions, we compare three different situations: risk, scenario ambiguity and frequency ambiguity. We show that risk and risk aversion significantly reduce the optimal cutting age. We also show that both scenario and frequency ambiguities reinforce the effect of risk. Inversely, ambiguity aversion has no effect. The value of information that resolves scenario ambiguity is high, whereas it is null for frequency ambiguity. 
Keywords:  Rotation decision,Risk,Ambiguity,Ambiguity Aversion,Risk Aversion,Value of Information,Forests,Faustmann criterion 
Date:  2022–10–04 
URL:  http://d.repec.org/n?u=RePEc:hal:wpaper:hal03796414&r=upt 
By:  Naomi FriedmanSokuler (BarIlan University [Israël]); Claudia Senik (PSE  Paris School of Economics  UP1  Université Paris 1 PanthéonSorbonne  ENSPSL  École normale supérieure  Paris  PSL  Université Paris sciences et lettres  EHESS  École des hautes études en sciences sociales  ENPC  École des Ponts ParisTech  CNRS  Centre National de la Recherche Scientifique  INRAE  Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, PJSE  Paris Jourdan Sciences Economiques  UP1  Université Paris 1 PanthéonSorbonne  ENSPSL  École normale supérieure  Paris  PSL  Université Paris sciences et lettres  EHESS  École des hautes études en sciences sociales  ENPC  École des Ponts ParisTech  CNRS  Centre National de la Recherche Scientifique  INRAE  Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, SU  Sorbonne Université) 
Abstract:  Using the American and the French timeuse surveys, we examine whether people have a preference for a more diversified mix of activities, in the sense that, everything else equal, they experience a higher level of wellbeing when their agenda is multiactivity, rather than concentrated on a very small number of activities. This could be due to decreasing marginal utility, as is assumed for the consumption of goods, if each episode of time is conceived as yielding a certain level of utility per se. However, in the presence of returns to specialization, people would face a tradeoff between the efficiency of specialization and the taste for diversity, as concerns time arrangements. We test these hypotheses and investigate potential gender differences with regard to these patterns. 
Keywords:  Time allocation,Timeuse diversity,Subjective wellbeing,Life satisfaction,Momentary utility,Gender Time allocation,Gender 
Date:  2022–10 
URL:  http://d.repec.org/n?u=RePEc:hal:psewpa:halshs03828272&r=upt 
By:  André Casajus (HHL  Handelshochschule Leipzig  Graduate School of Management); Rodrigue Tido Takeng (CREM  Centre de recherche en économie et management  UNICAEN  Université de Caen Normandie  NU  Normandie Université  UR1  Université de Rennes 1  UNIVRENNES  Université de Rennes  CNRS  Centre National de la Recherche Scientifique) 
Abstract:  We introduce the concepts of the components' secondorder productivities in cooperative games with transferable utility (TU games) with a coalition structure (CS games) and of the components' secondorder payoffs for onepoint solutions for CS games as generalizations of the players' secondorder productivities in TU games and of the players' secondorder payoffs for onepoint solutions for TU games (Casajus in Discrete Appl Math 304:212219, 2021). The players' secondorder productivities are conceptualized as secondorder marginal contributions, that is, how one player affects another player's marginal contributions to coalitions containing neither of them by entering these coalitions. The players' secondorder payoffs are conceptualized as the effect of one player leaving the game on the payoff of another player. Analogously, the components' secondorder productivities are conceptualized as their secondorder productivities in the game between components; the components' secondorder payoffs are conceptualized as their secondorder payoffs in the game between components. We show that the Owen value is the unique efficient onepoint solution for CS games that reflects the players' and the components' secondorder productivities in terms of their secondorder payoffs. 
Keywords:  TU game,Shapley value,Owen value,Secondorder marginal contributions,Secondorder payoffs 
Date:  2022 
URL:  http://d.repec.org/n?u=RePEc:hal:journl:hal03798448&r=upt 
By:  Jinwon Kim (Department of Economics, Sogang University, Seoul, Korea); Jucheol Moon (Department of Computer Engineering & Computer Science, California State University, Long Beach) 
Abstract:  This paper aims to quantify congestion costs and estimate the scheduling utility function for commuters. To do so, we construct California commuters' traveltime profiles, namely, the menu of travel times that each individual will likely face according to alternate trip timing choices. On average, California commuters waste about 5 minutes per morning commute due to congestion. Commuters facing a higher congestion level at the peak hour tend to avoid congestion delays by arriving at an inconvenient edge time. We also discover that for the majority of the commuters in our data, traveltime profiles are much atter than our estimated schedule utility. From this finding, we question the accuracy of the existing bottleneck models in quantifying the economic costs of congestion and the optimal toll to ameliorate congestion. 
Keywords:  congestion costs; scheduling preference; commuting; Google Maps; big data; machinelearning 
JEL:  R41 R48 C8 C25 H21 
Date:  2022 
URL:  http://d.repec.org/n?u=RePEc:sgo:wpaper:2201&r=upt 
By:  Jérôme GarnierBrun; J.P. Bouchaud; Michael Benzaquen (LadHyX  Laboratoire d'hydrodynamique  X  École polytechnique  CNRS  Centre National de la Recherche Scientifique) 
Abstract:  The Slutsky equation, central in consumer choice theory, is derived from the usual hypotheses underlying most standard models in Economics, such as full rationality, homogeneity, and absence of interactions. We present a statistical physics framework that allows us to relax such assumptions. We first derive a general fluctuationresponse formula that relates the Slutsky matrix to spontaneous fluctuations of consumption rather than to response to changing prices and budget. We then show that, within our hypotheses, the symmetry of the Slutsky matrix remains valid even when agents are only boundedly rational but noninteracting. We then propose a model where agents are influenced by the choice of others, leading to a phase transition beyond which consumption is dominated by herding (or "fashion") effects. In this case, the individual Slutsky matrix is no longer symmetric, even for fully rational agents. The vicinity of the transition features a peak in asymmetry. 
Date:  2022–10–04 
URL:  http://d.repec.org/n?u=RePEc:hal:wpaper:hal03797176&r=upt 
By:  Chiaki Hara (Kyoto University [Kyoto]); Sujoy Mukerji (QMUL  Queen Mary University of London); Frank Riedel (University of Bielefeld); JeanMarc Marc Tallon (PSE  Paris School of Economics  UP1  Université Paris 1 PanthéonSorbonne  ENSPSL  École normale supérieure  Paris  PSL  Université Paris sciences et lettres  EHESS  École des hautes études en sciences sociales  ENPC  École des Ponts ParisTech  CNRS  Centre National de la Recherche Scientifique  INRAE  Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, PJSE  Paris Jourdan Sciences Economiques  UP1  Université Paris 1 PanthéonSorbonne  ENSPSL  École normale supérieure  Paris  PSL  Université Paris sciences et lettres  EHESS  École des hautes études en sciences sociales  ENPC  École des Ponts ParisTech  CNRS  Centre National de la Recherche Scientifique  INRAE  Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement) 
Abstract:  We investigate consequences of ambiguity on efficient allocations in an exchange economy. Ambiguity is embodied in the model uncertainty perceived by the consumers: they are unsure what would be the appropriate probability measure to apply to evaluate consumption and keep in consideration a set P of alternative probabilistic laws. Consumers are heterogeneously ambiguity averse with smooth 
Date:  2022–10 
URL:  http://d.repec.org/n?u=RePEc:hal:psewpa:halshs03828305&r=upt 