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on Utility Models and Prospect Theory |
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Issue of 2022‒11‒14
eight papers chosen by |
| By: | Paolo Leonetti |
| Abstract: | Let $\succsim$ be a binary relation on the set of simple lotteries over a countable outcome set $Z$. We provide necessary and sufficient conditions on $\succsim$ to guarantee the existence of a set $U$ of von Neumann--Morgenstern utility functions $u: Z\to \mathbf{R}$ such that $$ p\succsim q \,\,\,\Longleftrightarrow\,\,\, \mathbf{E}_p[u] \ge \mathbf{E}_q[u] \,\text{ for all }u \in U $$ for all simple lotteries $p,q$. In such case, the set $U$ is essentially unique. Then, we show that the analogue characterization does not hold if $Z$ is uncountable. This provides an answer to an open question posed by Dubra, Maccheroni, and Ok in [J. Econom. Theory~\textbf{115} (2004), no.~1, 118--133]. Lastly, we show that different continuity requirements on $\succsim$ allow for certain restrictions on the possible choices of the set $U$ of utility functions (e.g., all utility functions are bounded), providing a wide family of expected multi-utility representations. |
| Date: | 2022–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2210.04739&r=upt |
| By: | Yan Dolinsky |
| Abstract: | In this paper we develop the duality theory for the exponential utility maximization problem where trading is subject to quadratic transaction costs and the investor is required to liquidate her position at the maturity date. As an application of the constructed duality theory, we treat utility based hedging in the Bachelier model. For Europeans contingent claims with quadratic payoff we compute explicitly the optimal trading strategy. |
| Date: | 2022–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2210.03917&r=upt |
| By: | Anuradha M. Annaswamy; Vineet Jagadeesan Nair |
| Abstract: | Several examples of Cyber-physical human systems (CPHS) include real-time decisions from humans as a necessary building block for the successful performance of the overall system. Many of these decision-making problems necessitate an appropriate model of human behavior. Tools from Utility Theory have been used successfully in several problems in transportation for resource allocation and balance of supply and demand \citep{ben1985discrete}. More recently, Prospect Theory has been demonstrated as a useful tool in behavioral economics and cognitive psychology for deriving human behavioral models that characterize their subjective decision-making in the presence of stochastic uncertainties and risks, as an alternative to conventional Utility Theory \citep{kahneman_prospect_2012}. These models will be described in this article. Theoretical implications of Prospect Theory are also discussed. Examples will be drawn from transportation use cases such as shared mobility to illustrate these models as well as the distinctions between Utility Theory and Prospect Theory. |
| Date: | 2022–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2210.07322&r=upt |
| By: | Ponthiere, Gregory |
| Abstract: | Nozick's "utility monster" - a being who is more efficient than other persons at transforming resources into well-being - is often regarded as deeply impossible, on the ground of the incapacity of a single person to have a life that is better than a large number of other lives. In this article, I defend a purely marginalist view of the "utility monster", that is, that the primary characteristic of a "utility monster" is a higher sensitivity, at the margin, of well-being to resources, rather than a larger total well-being. I propose three purely marginalist accounts of "utility monster" and I introduce the related concept of "collective utility monster", in order to account for the collective predation of (almost) all resources by a group of persons. I argue that, although a long-lived person, if taken separately, could hardly belong to the category of "utility monster", a large group of long-lived persons can, under some conditions, belong to the category of "collective utility monster". In the light of the increasingly large proportion of cohorts reaching very old ages nowadays, Nozick's objection against utilitarianism turns out, after a thorough review, to be most relevant for real-world aging societies. |
| Keywords: | longevity,mortality,inequalities,utilitarianism,Nozick's utility monster |
| JEL: | I31 J10 J18 |
| Date: | 2022 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:glodps:1186&r=upt |
| By: | David Baqaee; Ariel Burstein; Yasutaka Koike-Mori |
| Abstract: | We show how to recover the money-metric utility function, which converts income at one point in time into equivalent income at another point in time, using repeated cross-sectional household data. Our procedure allows unrestricted preferences, but requires that households’ preferences be the same in both the cross-section and the time-series. In prior work, Jaravel and Lashkari (2022) provide a solution to this problem. We leverage a different theoretical insight to address this problem. Our idea is to trace out Hicksian (or compensated) demand curves through time by matching households on the same indifference curve at different points in time. Given Hicksian demand curves, we can construct cost-of-living indices and money-metric utility for every matched income level. We apply our method to household consumption survey data from the United Kingdom from 1974 to 2017. We find that the official annual inflation rate understates welfare-relevant inflation for the poorest households by around half a percentage point per year and overstates it for the richest households by around a quarter of a percentage point per year. |
| JEL: | E01 E31 |
| Date: | 2022–10 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:30549&r=upt |
| By: | Kexin Chen; Hoi Ying Wong |
| Abstract: | In this paper, we investigate an optimal consumption--investment problem in which the unobserved stock trend is modulated by a hidden Markov chain, representing different economic regimes. In the classical approach, the hidden state is estimated from historical asset prices, but recent technology enables investors to consider alternative data when making decisions. These include social media commentary, expert opinions, pandemic data, and GPS data, which originate outside of the standard repertoire of market data but are considered useful for predicting stock trends. We model the asset price and alternative data series as a diffusion process and a jump-diffusion process, respectively. By incorporating the alternative data into the filtering process, we extend the Wonham filter to a degenerate jump diffusion with L\'{e}vy-type jumps. This introduces major analytical challenge to the corresponding stochastic control problem. We address this by taking a novel duality approach. We link the dual problem to an optimization problem over a set of equivalent local martingale measures and devise a methodology to obtain the optimal solution using a filtering technique with the alternative data. We show that the dual problem provides a unique smooth solution for constant relative risk aversion (CRRA) utility functions. In addition, we obtain an explicit feedback optimal consumption--investment strategy through the advantages provided by the alternative data. |
| Date: | 2022–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2210.08422&r=upt |
| By: | Chatterjee, Sidharta |
| Abstract: | The goal of this paper is to examine and analyze how certain factors influence our social decision making process. I undertake an investigative study into the dynamics of rational choice theory which is behind making decisions rationally productive. The research touches on the foundational concepts of Social Choice Rationality—the theory that is grounded on searching and making choices socially rational for the decision maker. The welfare functional component of social choice theory underlying rational decision making have been examined, and new knowledge have been derived from the analysis that could be helpful for making collective decisions which concern public policy and social welfare. |
| Keywords: | Decision choice, rational choice theory, rational intelligence, social choice theory, social choice rationality. |
| JEL: | I3 I30 I31 |
| Date: | 2022–10–16 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:114985&r=upt |
| By: | Back, Camila (LMU Munich); Spann, Martin (LMU Munich) |
| Abstract: | Customer satisfaction is an important metric to predict customer behavior and as a result firms' profitability. Expectations of a product's performance serve as a reference point against which customers evaluate their satisfaction with the products' actual performance. However, what is the effect of uncertainty in expectations? This paper develops a novel theoretical model of satisfaction, in which expectations reflect distributions of individual beliefs about performance outcomes. Based on this model, uncertainty shifts subjective reference points upward. That is, uncertainty increases the performance level at which customers switch from being dissatisfied to being satisfied. Furthermore, uncertainty has an attenuating effect on both positive and negative deviations of actual performance from subjective reference points. Put differently, a bad performance feels less bad and a good performance feels less good when it is expected, compared with unexpected. The authors find support for the model's predictions in an experimental study on product delivery as well as a field study based on online reviews. In addition, the authors develop a model-based tool that predicts the effect of uncertainty on customer satisfaction across different customizable scenarios. The paper's results carry implications for firms' communication, customer valuation and recovery strategies. |
| Keywords: | customer satisfaction; uncertainty; probabilistic beliefs; prospect theory; |
| Date: | 2022–10–24 |
| URL: | http://d.repec.org/n?u=RePEc:rco:dpaper:343&r=upt |