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on Utility Models and Prospect Theory |
| By: | Canishk Naik; Daniel Reck |
| Abstract: | We consider the optimal policy problem of a benevolent planner, who is uncertain about an individual's true preferences because of inconsistencies in revealed preferences across behavioral frames. We adapt theories of expected utility maximization and ambiguity aversion to characterize the planner's objective, which results in welfarist criteria similar to social welfare functions, with intrapersonal frames replacing interpersonal types. Under paternalistic risk aversion or ambiguity aversion, a policy is less desirable to the planner, holding all else fixed, when it leads to more disagreement about welfare from revealed preferences. We map some examples of behavioral models into our framework and describe how this notion of robustness plays out in applied settings. |
| JEL: | D60 H0 I3 |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:nbr:nberwo:32813 |
| By: | Hasanjan Sayit |
| Abstract: | We prove that weak convergence within generalized gamma convolution (GGC) distributions implies convergence in the mean value. We use this fact to show the robustness of the expected utility maximizing optimal portfolio under exponential utility function when return vectors are modelled by hyperbolic distributions. |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2407.15105 |
| By: | Makoto Abe (Faculty of Economcis, The University of Tokyo) |
| Abstract: | In economics, uncertainty is distinguished into two types: risk, which can be evaluated in terms of probability, and ambiguity, in which the probability is unknown. In decision making under risk, the rational course of action is to make a choice that maximizes expected utility, which is the utility of an event weighted by its probability. On the other hand, under ambiguity, where the probability is unknown, how should decisions be made? We first introduce the Minimax Regret, a decision-making criterion under ambiguity where probabilities are unknown but the interval is known. As a concrete example, consider two slot machines: one existing and one new. The winning probability of the former is known, while the winning probability of the latter is unknown, with only the interval provided. In this case, the optimal strategy according to the Minimax Regret criterion would be to randomly pull each of the two slot machines with a certain probability. Next, when utility is measured by a long-term metric, the interval of uncertainty for this metric decreases over time. To address this, we introduce the Adaptive Minimax Regret (AMR) approach, which maximizes utility by updating the probabilities according to the Minimax Regret criterion based on the information available at each point in time. Simulation testing on the case of the existing and new slot machines mentioned earlier showed that AMR produced high performance comparable to bandit algorithms. As an application of AMR in marketing, we propose sequential campaign strategies and probabilistic A/B testing aimed at maximizing the average customer lifetime (utility) of the target audience. |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:tky:fseres:2024cf1234 |
| By: | Harin, Alexander |
| Abstract: | Old problems of the mathematical description of the economical behavior of a man are briefly reviewed. They are the comparison of choices of a man between uncertain and sure games and the radically different behavior of a man in different domains. The proposed solution of the problems consists in the purely mathematical method and models and is briefly reviewed in the Appendix. In the present paper the main attention is paid to the analysis of the experimental support of this possible solution. The generally accepted random incentive experimental procedures are discussed. A “certain-uncertain” inconsistency between the certain type of the choices and the uncertain type of the incentives is revealed and analyzed. |
| Keywords: | utility; prospect theory; experiment; incentive; random-lottery incentive system; Prelec; probability weighting function; |
| JEL: | C1 C9 D8 D81 |
| Date: | 2024–08–17 |
| URL: | https://d.repec.org/n?u=RePEc:pra:mprapa:121756 |
| By: | Uri Gneezy; Yoram Halevy; Brian Hall; Theo Offerman; Jeroen van de Ven |
| Abstract: | Researchers in behavioral and experimental economics often argue that only incentive-compatible mechanisms can elicit effort and truthful responses from participants. Others argue that participants make less-biased decisions when the stakes are sufficiently high. Are these claims correct? We investigate the change in behavior as incentives are scaled up in the Allais paradox, and document an increase , not decrease, in deviations from expected utility with higher stakes. We also find that if one needs to approximate participants’ behavior in real high-stakes Allais (which are often too expensive to conduct), it is better to use hypothetically high stakes than real low stakes, as is typically the practice today. |
| Keywords: | high stakes, real and hypothetical incentives, Allais paradox, Expected Utility |
| JEL: | C91 D81 |
| Date: | 2024–08–17 |
| URL: | https://d.repec.org/n?u=RePEc:tor:tecipa:tecipa-783 |
| By: | Mu Lin; Di Zhang; Ben Chen; Hang Zheng |
| Abstract: | Water market is a contemporary marketplace for water trading and is deemed to one of the most efficient instruments to improve the social welfare. In modern water markets, the two widely used trading systems are an improved pair-wise trading, and a 'smart market' or common pool method. In comparison with the economic model, this paper constructs a conceptual mathematic model through the HARA utility functions. Mirroring the concepts such as Nash Equilibrium, Pareto optimal and stable matching in economy, three significant propositions are acquired which illustrate the advantages of the common pool method compared with the improved pair-wise trading. |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2408.05194 |
| By: | Le, V.D.; Pham, L.T. |
| Abstract: | The paper is aimed at measuring the risk attitude of maize farmers and testing the relationship between farmers' risk attitudes and optimal use of inputs in production. The experimental method of Eckel and Grossman (2002) associated with the constant partial risk utility function was employed to measure the farmers’ risk attitude. Then, allocative efficiency coefficients were calculated from the output elasticities of inputs estimated from the Cobb-Douglas production function associated with the profit-maximizing condition in using inputs. The data was collected from a survey of 130 farm households located in large and concentrated maize production areas in the Mekong Delta. It is found that the majority of farmers are found to be risk-averse, accounting for 69.05%. Generally, the more risk averse the farmers are, the less purchased inputs are used in production. Then, most of farmers are not able to maximize profits. |
| Keywords: | Crop Production/Industries, Production Economics, Risk and Uncertainty |
| Date: | 2024–04–28 |
| URL: | https://d.repec.org/n?u=RePEc:ags:asea24:344440 |
| By: | Katia Colaneri; Daniele Mancinelli; Immacolata Oliva |
| Abstract: | In this paper, we investigate an optimal investment problem associated with proportional portfolio insurance (PPI) strategies in the presence of jumps in the underlying dynamics. PPI strategies enable investors to mitigate downside risk while still retaining the potential for upside gains. This is achieved by maintaining an exposure to risky assets proportional to the difference between the portfolio value and the present value of the guaranteed amount. While PPI strategies are known to be free of downside risk in diffusion modeling frameworks with continuous trading, see e.g., Cont and Tankov (2009), real market applications exhibit a significant non-negligible risk, known as gap risk, which increases with the multiplier value. The goal of this paper is to determine the optimal PPI strategy in a setting where gap risk may occur, due to downward jumps in the asset price dynamics. We consider a loss-averse agent who aims at maximizing the expected utility of the terminal wealth exceeding a minimum guarantee. Technically, we model agent's preferences with an S-shaped utility functions to accommodate the possibility that gap risk occurs, and address the optimization problem via a generalization of the martingale approach that turns to be valid under market incompleteness in a jump-diffusion framework. |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2407.21148 |
| By: | Zixin Feng; Dejian Tian; Harry Zheng |
| Abstract: | The paper investigates the consumption-investment problem for an investor with Epstein-Zin utility in an incomplete market. A non-Markovian environment with unbounded parameters is considered, which is more realistic in practical financial scenarios compared to the Markovian setting. The optimal consumption and investment strategies are derived using the martingale optimal principle and quadratic backward stochastic differential equations (BSDEs) whose solutions admit some exponential moment. This integrability property plays a crucial role in establishing a key martingale argument. In addition, the paper also examines the associated dual problem and several models within the specified parameter framework. |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2407.19995 |
| By: | V. G. Bardakhchyan; A. E. Allahverdyan |
| Abstract: | We solve the two-player bargaining problem using Weber's law in psychophysics, which is applied to the perception of utility changes. By applying this law, one of the players (or both of them) defines lower and upper utility thresholds, such that once the lower threshold is established, bargaining continues in the inter-threshold domain where the solutions are acceptable to both parties. This provides a sequential solution to the bargaining problem, and it can be implemented iteratively reaching well-defined outcomes. The solution is Pareto-optimal, symmetric, and is invariant to affine-transformations of utilities. For susceptible players, iterations are unnecessary, so they converge in one stage toward the (axiomatic) Nash solution of the bargaining problem. This situation also accounts for the asymmetric Nash solution, where the weights of each player are expressed via their Weber constants. Thus the Nash solution is reached without external arbiters and without requiring the independence of irrelevant alternatives. For non-susceptible players our approach leads to different results. |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2408.02492 |
| By: | Chung-Han Hsieh; Jie-Ling Lu |
| Abstract: | Solving large-scale robust portfolio optimization problems is challenging due to the high computational demands associated with an increasing number of assets, the amount of data considered, and market uncertainty. To address this issue, we propose an extended supporting hyperplane approximation approach for efficiently solving a class of distributionally robust portfolio problems for a general class of additively separable utility functions and polyhedral ambiguity distribution set, applied to a large-scale set of assets. Our technique is validated using a large-scale portfolio of the S&P 500 index constituents, demonstrating robust out-of-sample trading performance. More importantly, our empirical studies show that this approach significantly reduces computational time compared to traditional concave Expected Log-Growth (ELG) optimization, with running times decreasing from several thousand seconds to just a few. This method provides a scalable and practical solution to large-scale robust portfolio optimization, addressing both theoretical and practical challenges. |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2408.07879 |
| By: | Joan Costa-Font; Frank Cowell; Joan Costa-i-Font |
| Abstract: | An individual’s inequality aversion (IA) is a central preference parameter that captures the welfare sacrifice from exposure to inequality. However, it is far from trivial how to best elicit IA estimates. Also, little is known about the behavioural determinants of IA and how they differ across domains such as income and health. Using representative surveys from England, this paper elicits comparable estimates of IA in the health and income domains using two alternative elicitation techniques: a direct trade-off and an indirect “imaginary-grandchild” approach that results from the choices between hypothetical lotteries. We make three distinct contributions to the literature. First, we show that IA systematically differs between income and health domains. Average estimates are around 0.8 for income IA and range from 0.8 to 1.5 for health IA. Second, we find that risk aversion and locus of control are central determinants of IA in both income and health domains. Finally, we present evidence suggesting that the distribution and comparison of IA vary depending on the elicitation method employed. |
| Keywords: | inequality aversion, income inequality aversion, health inequality aversion, imaginary grandchild, inequality and efficiency trade-offs, risk attitudes |
| JEL: | H10 I18 |
| Date: | 2024 |
| URL: | https://d.repec.org/n?u=RePEc:ces:ceswps:_11261 |
| By: | Peng Liu; Andreas Tsanakas; Yunran Wei |
| Abstract: | In this paper, we study the risk sharing problem among multiple agents using Lambda value at risk as their preferences under heterogenous beliefs, where the beliefs are represented by several probability measures. We obtain semi-explicit formulas for the inf-convolution of multiple Lambda value at risk under heterogenous beliefs and the explicit forms of the corresponding optimal allocations. To show the interplay among the beliefs, we consider three cases: homogeneous beliefs, conditional beliefs and absolutely continuous beliefs. For those cases, we find more explicit expressions for the inf-convolution, showing the influence of the relation of the beliefs on the inf-convolution. Moreover, we consider the inf-convolution of one Lambda value at risk and a general risk measure, including expected utility, distortion risk measures and Lambda value at risk as special cases, with different beliefs. The expression of the inf-convolution and the form of the optimal allocation are obtained. Finally, we discuss the risk sharing for another definition of Lambda value at risk. |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2408.03147 |
| By: | Christoph Czichowsky; Martin Herdegen; David Martins |
| Abstract: | We revisit the classical topic of quadratic and linear mean-variance equilibria with both financial and real assets. The novelty of our results is that they are the first allowing for equilibrium prices driven by general semimartingales and hold in discrete as well as continuous time. For agents with quadratic utility functions, we provide necessary and sufficient conditions for the existence and uniqueness of equilibria. We complement our analysis by providing explicit examples showing non-uniqueness or non-existence of equilibria. We then study the more difficult case of linear mean-variance preferences. We first show that under mild assumptions, a linear mean-variance equilibrium corresponds to a quadratic equilibrium (for different preference parameters). We then use this link to study a fixed-point problem that establishes existence (and uniqueness in a suitable class) of linear mean-variance equilibria. Our results rely on fine properties of dynamic mean-variance hedging in general semimartingale markets. |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2408.03134 |
| By: | Liu, Pengcheng; Xie, Qing; You, Yi; Dong, Qingqing |
| Abstract: | Consumers are presented with increasingly difficult choice tasks and are experiencing more choice overload during the decision-making process. Based on the emotion-imbued choice model and incorporating subjective state consequences into the framework of experienced utility, this research constructed a systematic scale to measure choice overload in several decision-making stages. This research conducted three experiments using liquid milk as a consumption product to test whether choice overload would be influenced by increasing the number of attributes, adding similar options, and information nudges, and whether this effect would be heterogeneous in consumer characteristics. Results indicate that more attributes and the addition of similar options would increase the perceived difficulty of choice and result in negative emotions, while information nudges might lessen choice overload and help consumers make decisions. Besides, consumers’ pursuit of maximization also determines their perceived choice overload; maximizers are more likely to experience choice overload than satisficers. |
| Keywords: | Consumer/Household Economics, Food Consumption/Nutrition/Food Safety |
| Date: | 2024–08–07 |
| URL: | https://d.repec.org/n?u=RePEc:ags:cfcp15:344272 |
| By: | Babette Jansen (University of Antwerp); Roland Winkler (Friedrich Schiller University Jena, and University of Antwerp) |
| Abstract: | We consider a two-agent New Keynesian model with savers and hand-to-mouth households with quasi-separable utility functions as introduced by Bilbiie (2020a). This framework allows for separate parameterization of consumption-hours complementarity and income effects on labor supply. We examine how variations in the size of income effects, the degree of non-separability between consumption and hours worked, and the share of hand-to-mouth households impact aggregate dynamics and determinacy properties of interest rate rules. Complementarity between consumption and hours worked and small income effects can reverse the Taylor principle and result in expansionary monetary contractions. |
| Keywords: | Heterogeneity, Monetary policy, Nonseparable preferences, Real indeterminacy, Taylor principle, TANK |
| JEL: | E32 E52 E58 E44 E24 |
| Date: | 2024–08–23 |
| URL: | https://d.repec.org/n?u=RePEc:jrp:jrpwrp:2024-006 |
| By: | Marc Fleurbaey; Eduardo Zambrano |
| Abstract: | Imagine that a large increment can be given to an individual in a society. We ask: what is the maximal sacrifice that can be imposed on another individual according to an evaluator for the sake of this increment? We show that the answer can reveal how inequality averse an evaluator is. In particular, all Kolm-Pollak evaluators would sacrifice the full income of the sacrificed individual if their income was low enough and a declining fraction of their income otherwise. Kolm-Atkinson evaluators would sacrifice the full income of the sacrificed individual, for all income levels, if their inequality aversion was no greater than one, and sacrifice a constant fraction of their income otherwise. Motivated by these findings, we propose a class of social preferences that, starting from a baseline level of protection, protect a higher fraction of the sacrificed individual's income the lower their income. In addition to relating levels of protected income to coefficients of inequality, we also characterize the classes of additively separable social welfare functions that guarantee specific (absolute or relative) levels of protection. |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2408.04814 |