|
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 continuous-time pre-commitment 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 second-order distribution (SOD). The KMM model separates risk attitudes and ambiguity attitudes apart and the aim of the DM is to maximize the two-fold 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 one-fold expected utility problem on the second-order 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 semi-explicit 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 Black-Scholes 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 continuous-time 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: | Continuous-Time 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:e-22-009&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:hal-03796414&r=upt |
| By: | Naomi Friedman-Sokuler (Bar-Ilan University [Israël]); Claudia Senik (PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - 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 Panthéon-Sorbonne - ENS-PSL - 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 time-use 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 well-being when their agenda is multi-activity, 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 trade-off 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,Time-use diversity,Subjective well-being,Life satisfaction,Momentary utility,Gender Time allocation,Gender |
| Date: | 2022–10 |
| URL: | http://d.repec.org/n?u=RePEc:hal:psewpa:halshs-03828272&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 - UNIV-RENNES - Université de Rennes - CNRS - Centre National de la Recherche Scientifique) |
| Abstract: | We introduce the concepts of the components' second-order productivities in cooperative games with transferable utility (TU games) with a coalition structure (CS games) and of the components' second-order payoffs for one-point solutions for CS games as generalizations of the players' second-order productivities in TU games and of the players' second-order payoffs for one-point solutions for TU games (Casajus in Discrete Appl Math 304:212-219, 2021). The players' second-order productivities are conceptualized as second-order 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' second-order payoffs are conceptualized as the effect of one player leaving the game on the payoff of another player. Analogously, the components' second-order productivities are conceptualized as their second-order productivities in the game between components; the components' second-order payoffs are conceptualized as their second-order payoffs in the game between components. We show that the Owen value is the unique efficient one-point solution for CS games that reflects the players' and the components' second-order productivities in terms of their second-order payoffs. |
| Keywords: | TU game,Shapley value,Owen value,Second-order marginal contributions,Second-order payoffs |
| Date: | 2022 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:hal-03798448&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' travel-time 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, travel-time 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 Garnier-Brun; 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 fluctuation-response 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 non-interacting. 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:hal-03797176&r=upt |
| By: | Chiaki Hara (Kyoto University [Kyoto]); Sujoy Mukerji (QMUL - Queen Mary University of London); Frank Riedel (University of Bielefeld); Jean-Marc Marc Tallon (PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - 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 Panthéon-Sorbonne - ENS-PSL - 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:halshs-03828305&r=upt |