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on Utility Models and Prospect Theory |
| By: | Chow, Nikolai Sheung-Chi |
| Abstract: | This study advances the understanding of risk measures and portfolio choice for investors exhibiting gain-loss dependent risk attitudes by integrating stochastic dominance (SD) concepts, including prospect stochastic dominance (PSD) and Markowitz stochastic dominance (MSD). We demonstrate that partial moments serve as effective risk measures, aligning with various SD criteria to capture diverse investor attitudes toward gains and losses. One contribution of this paper is the development of a decision-making criterion to identify the segment of the mean-variance efficient frontier that is efficient under different SD conditions, applicable to elliptical distributions. Leveraging partial moments, we adopt a portfolio optimization method that constructs portfolios dominating a benchmark from multiple SD perspectives, facilitating comparisons across gain-loss utility models. This approach enables a more direct comparison of alternative gain-loss utility models without relying on parameter assumptions, which often lead to differing risk-return priorities within a model. |
| Keywords: | Gain-Loss Utility, Mean-Variance Analysis, Stochastic Dominance, Partial Moments, Prospect Theory |
| JEL: | C0 G0 |
| Date: | 2025–04–17 |
| URL: | https://d.repec.org/n?u=RePEc:pra:mprapa:124440 |
| By: | Mario Ghossoub; Bin Li; Benxuan Shi |
| Abstract: | We consider a monopoly insurance market with a risk-neutral profit-maximizing insurer and a consumer with Yaari Dual Utility preferences that distort the given continuous loss distribution. The insurer observes the loss distribution but not the risk attitude of the consumer, proxied by a distortion function drawn from a continuum of types. We characterize the profit-maximizing, incentive-compatible, and individually rational menus of insurance contracts, show that equilibria are separating, and provide key properties thereof. Notably, insurance coverage and premia are monotone in the level of risk aversion; the most risk-averse consumer receives full insurance $(\textit{efficiency at the top})$; the monopoly absorbs all surplus from the least-risk averse consumer; and consumers with a higher level of risk aversion induce a higher expected profit for the insurer. Under certain regularity conditions, equilibrium contracts can be characterized in terms of the marginal loss retention per type of consumer, and they consist of menus of layered deductible contracts, where each such layered structure is determined by the risk type of the consumer. In addition, we examine the effect of a fixed insurance provision cost on equilibria. We show that if the fixed cost is prohibitively high, then there will be no $\textit{ex ante}$ gains from trade. However, when trade occurs, separating equilibrium contracts always outperform pooling equilibrium contracts, and they are identical to those obtained in the absence of fixed costs, with the exception that only part of the menu is excluded. The excluded contracts are those designed for consumers with relatively lower risk aversion, who are less valuable to the insurer. Finally, we characterize incentive-efficient menus of contracts in the context of an arbitrary type space. |
| Date: | 2025–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2504.01095 |
| By: | Yiding Feng; Wei Tang |
| Abstract: | We introduce and study the persuasive calibration problem, where a principal aims to provide trustworthy predictions about underlying events to a downstream agent to make desired decisions. We adopt the standard calibration framework that regulates predictions to be unbiased conditional on their own value, and thus, they can reliably be interpreted at the face value by the agent. Allowing a small calibration error budget, we aim to answer the following question: what is and how to compute the optimal predictor under this calibration error budget, especially when there exists incentive misalignment between the principal and the agent? We focus on standard Lt-norm Expected Calibration Error (ECE) metric. We develop a general framework by viewing predictors as post-processed versions of perfectly calibrated predictors. Using this framework, we first characterize the structure of the optimal predictor. Specifically, when the principal's utility is event-independent and for L1-norm ECE, we show: (1) the optimal predictor is over-(resp. under-) confident for high (resp. low) true expected outcomes, while remaining perfectly calibrated in the middle; (2) the miscalibrated predictions exhibit a collinearity structure with the principal's utility function. On the algorithmic side, we provide a FPTAS for computing approximately optimal predictor for general principal utility and general Lt-norm ECE. Moreover, for the L1- and L-Infinity-norm ECE, we provide polynomial-time algorithms that compute the exact optimal predictor. |
| Date: | 2025–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2504.03211 |
| By: | Thomas Boyer-Kassem (MAPP [Poitiers] - Métaphysique allemande et philosophie pratique - UP - Université de Poitiers = University of Poitiers); Sébastien Duchêne (CEE-M - Centre d'Economie de l'Environnement - Montpellier - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement - Institut Agro Montpellier - Institut Agro - Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement - UM - Université de Montpellier) |
| Abstract: | In some applications to human beings, the precautionary principle seems to raise specific ethical concerns. For instance, it has been used by a business owner in a court of justice to justify his refusal to hire applicants with a certain geographical origin for safety reasons. Or in public management, the precautionary principle has been used to exclude men who have sexual relations with men from donating blood on the basis of a higher HIV prevalence in this group. Does not the precautionary principle here amount to justifying a form of discrimination? To help analyze what is at stake from a decision-theoretic viewpoint and to consider the possibility of ethical catastrophes, we offer a lexical utility model of the precautionary principle, which generalizes a previous model by Bartha and DesRoches (Synthese 199:8701-8740, 2021), Steel and Bartha (Risk Anal https:// doi. org/ 10. 1111/ risa. 13892, 2022). Traditional expected utility theory also comes out as a special case of the model. Our proposal opens new perspectives for considering ethical dilemmas within a precautionary approach. It is intended to serve as a guiding tool for management teams in socially responsible companies, public institutions, and government agencies. |
| Keywords: | lexical utility, Precautionary principle, Discrimination, Ethics, Dilemma |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:hal:journl:hal-04992277 |
| By: | N. S. Gonchar |
| Abstract: | The state of economic theory and accumulated facts from the different branches of the economic science require to analyze the concept of the description of economy systems. The economic reality generates the problems the solution of that is only possible by a new paradigm of the description of economy system. The classical mathematical economics is based on a notion of the rational consumer choice generated by a certain preference relation on some set of goods a consumer wanted and the concept of maximization of the firm profit. The sense of the notion of the ratio- nal consumer choice is that it is determined by a certain utility function, defining the choice of a consumer by maximization of it on a certain budget set of goods. More- over, choices of consumers are independent. In the reality choices of consumers are not independent because they depend on the firms supply. Except the firms supply, the consumer choice is also determined by information about the state of the economy system that the consumer has and respectively eval- uates at the moment of the choice. In turn, the firms supply is made on the basis of needs of the consumers and their buying power. By information about the state of the economy system we understand a certain information about the equilibrium price vector and productive processes realized in the economy system under the equilibrium price vector. |
| Date: | 2025–03 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2503.24257 |
| By: | Pascal Stiefenhofer |
| Abstract: | This paper explores how ethical consumption can transform democratic governance toward sustainability by challenging traditional economic models centered on utility and efficiency. As societal values shift toward transparency equity and environmental responsibility ethical consumers increasingly influence markets. Drawing on Whites Kantian economic framework and Ingleharts theory of value change the paper proposes a model integrating moral imperatives into economic theory. Using a vector bundle approach it captures evolving ethical preferences advocating for an inclusive sustainability focused economic paradigm aligned with post materialist values. |
| Date: | 2025–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2504.01138 |
| By: | Alexandre Boistard; Laurence Carassus; Safae Issaoui |
| Abstract: | Drawing from set theory, this article contributes to a deeper understanding of the no-arbitrage principle in multiple-priors settings and its application in mathematical finance. In the quasi-sure discrete-time frictionless market framework of Bouchard and Nutz, the equivalence between the quasi-sure no-arbitrage condition and the existence of a probability measure for which the local one-prior no-arbitrage condition holds and the affine hull of the support is equal to the quasi-sure support, all of this in a quasi-sure sense, was established by Blanchard and Carassus. We aim to extend this result to the projective setup introduced by Carassus and Ferhoune. This setup allows for standardised measurability assumptions, in contrast to the framework of Bouchard and Nutz, where prices are assumed to be Borel measurable, strategies and stochastic kernels universally measurable, and the graphs of one-step priors analytic sets. To achieve this, we assume the classical axioms of Zermelo-Fraenkel set theory, including the axiom of choice (ZFC), supplemented by the Projective Determinacy (PD) axiom. In ZFC+PD the existence of such probability measures was assumed by Carassus and Ferhoune to prove the existence of solutions in a quasi-sure nonconcave utility maximisation problem. The equivalence with the quasi-sure no-arbitrage was only conjectured. |
| Date: | 2025–03 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2504.00158 |
| By: | Rosenmüller, Joachim (Center for Mathematical Economics, Bielefeld University) |
| Abstract: | We continue the discussion of the taxation game following our presentation in [12]. Our concept describes a cooperative game played between a set of jurisdictions (“ countries”). These players admit the operation of a multinational enterprise (MNE, the “firm”) within their jurisdiction. The original version of this game is due to W. F. Richter [3], [4]. We suggest an extension of the model by introducing the dual game of the firm’s profits and the tax function game. The latter is the NTU game generated by introducing tax functions (the term “tariffs” will be avoided henceforth). In [12] we treated the bargaining situation obtained when all countries decide to cooperate – otherwise everyone will fall back on their status quo point. However, in his basic paper, Richter argues that the share of the tax basis allotted to a country should be determined by the Shapley value of the taxation game. This idea establishes an interesting new field of applications. The Shapley value “as a tool in theoretical economics” [13], [14] has widely been applied in Game Theory, Equilibrium Theory, applications to Cost Sharing problems, Airport Landing Fee games, and many others. Based on these ideas, we continue our presentation by formulating the tax function game for the countries involved and introducing the Maschler–Perles–Shapley value as developed in [11]. To this end, we introduce the adjusted TU game, which reflects a rescaling of utility measurement as suggested by the superadditivity axiom of the Maschler–Perles solution. Then the Maschler–Perles–Shapley value of the tax function game is the image of the Shapley value of the adjusted TU game on the Pareto surface of the grand coalition. We demonstrate that the Maschler-Perles–Shapley value for the tax function game is Pareto efficient, covariant with affine transformations of utility, and anonymous. |
| Date: | 2025–04–23 |
| URL: | https://d.repec.org/n?u=RePEc:bie:wpaper:704 |
| By: | Jiakun Zheng (AMSE - Aix-Marseille 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); Yanyin Li |
| Abstract: | This paper utilizes data from the 2017 China Household Finance Survey (CHFS) to examine the impact of loss aversion on individuals' willingness to relocate due to environmental concerns. We find that individuals who are more loss averse are less likely to consider moving, resulting in what is called the status-quo bias. In addition, we find that individuals with stronger family ties as measured by the number of siblings and higher household fixed assets are more susceptible to these effects, implying that they are more attached to their current place of residence and less likely to relocate.We thank Ling Zhou and one anonymous referee for constructive comments. |
| Keywords: | Family ties, Status-quo bias, Loss aversion, Willingness to relocate |
| Date: | 2024–12–30 |
| URL: | https://d.repec.org/n?u=RePEc:hal:journl:hal-04991151 |
| By: | Motoki Otsuka |
| Abstract: | Graphon games are a class of games with a continuum of agents, introduced to approximate the strategic interactions in large network games. The first result of this study is an equilibrium existence theorem in graphon games, under the same conditions as those in network games. We prove the existence of an equilibrium in a graphon game with an infinite-dimensional strategy space, under the continuity and quasi-concavity of the utility functions. The second result characterizes Nash equilibria in graphon games as the limit points of asymptotic Nash equilibria in large network games. If a sequence of large network games converges to a graphon game, any convergent sequence of asymptotic Nash equilibria in these large network games also converges to a Nash equilibrium of the graphon game. In addition, for any graphon game and its equilibrium, there exists a sequence of large network games that converges to the graphon game and has asymptotic Nash equilibria converging to the equilibrium. These results suggest that the concept of a graphon game is an idealized limit of large network games as the number of players tends to infinity. |
| Date: | 2025–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2504.01944 |
| By: | Yike Wang |
| Abstract: | In this paper, we extend the research on time-consistent stochastic control problems with higher-order moments, as formulated by [Y. Wang et al. SIAM J. Control. Optim., 63 (2025), in press]. We consider a linear controlled dynamic equation with state-dependent diffusion, and let the sum of a conventional mean-variance utility and a fairly general function of higher-order central moments be the objective functional. We obtain both the sufficiency and necessity of the equilibrium condition for an open-loop Nash equilibrium control (ONEC), under some continuity and integrability assumptions that are more relaxed and natural than those employed before. Notably, we derive an extended version of the stochastic Lebesgue differentiation theorem for necessity, because the equilibrium condition is represented by some diagonal processes generated by a flow of backward stochastic differential equations whose the data do not necessarily satisfy the usual square-integrability. Based on the derived equilibrium condition, we obtain the algebra equation for a deterministic ONEC. In particular, we find that the mean-variance equilibrium strategy is an ONEC for our higher-order moment problem if and only if the objective functional satisfies a homogeneity condition. |
| Date: | 2025–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2504.04113 |
| By: | Ying Fan; Ziying Fan; Yiyi Zhou |
| Abstract: | This paper studies how dynamic changes in the search environment affect consumer search and purchase behavior. We develop a dynamic model that incorporates a non-stationary search environment and propose a feasible estimation procedure to estimate its parameters. We apply our model and estimation procedure to the Beijing housing market, utilizing detailed data on consumers’ complete search records. We show that accounting for dynamics is crucial for accurately estimating search costs. Additionally, we find that search environment dynamics have a significant impact on consumer decisions and welfare. Housing supply policies that alter search environment dynamics—by increasing the number of new listings and slowing down price increases—benefit consumers, primarily by incentivizing longer searches, more property visits, and ultimately leading to purchases that yield higher utility. |
| Keywords: | consumer search, non-stationary search environment, Beijing housing market |
| JEL: | D80 L80 R30 |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:ces:ceswps:_11709 |