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on Utility Models and Prospect Theory |
| By: | Mark Whitmeyer |
| Abstract: | I conduct a version of Rabin's (2000) calibration exercise in the subjective expected utility realm. I show that the rejection of some risky bet by a risk-averse agent only implies the rejection of more extreme and less desirable bets and nothing more. |
| Date: | 2024–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2412.18486 |
| By: | Chaitanya Joshi; Jinming Yang; Sergeja Slapnicar; Ryan K L Ko |
| Abstract: | Protecting against cyber-threats is vital for every organization and can be done by investing in cybersecurity controls and purchasing cyber insurance. However, these are interlinked since insurance premiums could be reduced by investing more in cybersecurity controls. The expected utility theory and the prospect theory are two alternative theories explaining decision-making under risk and uncertainty, which can inform strategies for optimizing resource allocation. While the former is considered a rational approach, research has shown that most people make decisions consistent with the latter, including on insurance uptakes. We compare and contrast these two approaches to provide important insights into how the two approaches could lead to different optimal allocations resulting in differing risk exposure as well as financial costs. We introduce the concept of a risk curve and show that identifying the nature of the risk curve is a key step in deriving the optimal resource allocation. |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2411.18838 |
| By: | Gerrit Bauch |
| Abstract: | The expected utility theorem of von Neumann and Morgenstern (1947) has been a milestone in economics, describing rational behavior by two axioms on a weak preference on lotteries on a finite set of outcomes: the Independence Axiom and the Continuity Axiom. For a weak preference fulfilling the Independence Axiom, I prove that continuity is equivalent to the existence of a set indifferent lotteries spanning a hyperplane. |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2411.17883 |
| By: | Silvana M. Pesenti; Steven Vanduffel; Yang Yang; Jing Yao |
| Abstract: | We study optimal payoff choice for an expected utility maximizer under the constraint that their payoff is not allowed to deviate ``too much'' from a given benchmark. We solve this problem when the deviation is assessed via a Bregman-Wasserstein (BW) divergence, generated by a convex function $\phi$. Unlike the Wasserstein distance (i.e., when $\phi(x)=x^2$). The inherent asymmetry of the BW divergence makes it possible to penalize positive deviations different than negative ones. As a main contribution, we provide the optimal payoff in this setting. Numerical examples illustrate that the choice of $\phi$ allow to better align the payoff choice with the objectives of investors. |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2411.18397 |
| By: | Ken-ichi Hashimoto; Ryonghun Im; Takuma Kunieda; Akihisa Shibata |
| Abstract: | By applying a simple dynamic general equilibrium model without exogenous shocks inhabited by infinitely lived capitalists and workers, we show that a higher degree of relative risk aversion can destabilize an economy. In traditional real business cycle (RBC) theory, a higher degree of relative risk aversion dampens the amplitude of the consumption fluctuations caused by exogenous shocks through consumption smoothing. However, a higher degree of relative risk aversion combined with a high degree of elasticity of the marginal product of capital can also lead to the emergence of a nonlinear mechanism that causes endogenous business fluctuations. The nontrivial steady state loses stability due to the higher degree of relative risk aversion; thus, endogenous business fluctuations can occur. This result suggests that for a deeper understanding of boom-bust cycles, researchers should merge exogenous and endogenous business fluctuations when investigating economies. |
| Date: | 2025–01 |
| URL: | https://d.repec.org/n?u=RePEc:dpr:wpaper:1272 |
| By: | Antony Millner |
| Abstract: | This paper investigates a duality between ambiguity averse preferences and the valuation of long run risky assets or public projects. The variational ambiguity model represents preferences over ambiguous acts via a minimization problem, and is fundamentally nonprobabilistic. In contrast, long run risky assets are ranked via a large maturity limit of expected discounted returns. Despite their apparent differences, we show that each variational ambiguity preference is a long run risk preference, and (under natural conditions) vice versa. We explore three implications: a notion of long run stochastic dominance that resolves differences between stochastic processes considered identical by standard risk measures, a typology of stochastic processes that pinpoints when a non-probabilistic description of long run risk is required, and an evolutionary foundation for variational ambiguity preferences that offers a novel explanation for ambiguity aversion. |
| JEL: | C73 D81 G12 H43 |
| Date: | 2024–12 |
| URL: | https://d.repec.org/n?u=RePEc:nbr:nberwo:33291 |
| By: | Jérôme Faure (CEBC - Centre d'Études Biologiques de Chizé - UMR 7372 - ULR - La Rochelle Université - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); Esther Devilliers (BETA - Bureau d'Économie Théorique et Appliquée - AgroParisTech - UNISTRA - Université de Strasbourg - Université de Haute-Alsace (UHA) - Université de Haute-Alsace (UHA) Mulhouse - Colmar - UL - Université de Lorraine - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement) |
| Abstract: | This article examines how integrating nature-based solutions into agricultural strategies can address the inefficient use of polluting technological solutions. A theoretical microeconomic model, based on subjective expected utility, is developed and empirically tested on rapeseed cultivation. The study highlights the overuse of polluting technological solutions and the underuse of nature-based solutions, driven by inaccurate perceptions of input productivity. The article provides recommendations for public policies aimed at correcting these perceptions and optimizing the use of inputs by balancing the cost-effectiveness of interventions for both nature-based and polluting technological solutions. The findings suggest that policies focused on correcting misperceptions about polluting technological solutions are more effective than those focused on nature-based solutions. |
| Keywords: | Input efficiency, Perception, Ecosystem service, Nature-based solutions, Subjective expected utility |
| Date: | 2023–08–29 |
| URL: | https://d.repec.org/n?u=RePEc:hal:journl:hal-04869177 |
| By: | Bernhard K Meister |
| Abstract: | Betting markets are gaining in popularity. Mean beliefs generally differ from prices in prediction markets. Logarithmic utility is employed to study the risk and return adjustments to prices. Some consequences are described. A modified payout structure is proposed. A simple asset price model based on flipping biased coins is investigated. It is shown using the Kullback-Leibler divergence how the misjudgment of the bias and the miscalculation of the investment fraction influence the portfolio growth rate. |
| Date: | 2024–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2412.14144 |
| By: | Nadia Gui\~naz\'u; Pablo Neme; Jorge Oviedo |
| Abstract: | This paper examines equilibria in dynamic two-sided matching games, extending Gale and Shapley's foundational model to a non-cooperative, decentralized, and dynamic framework. We focus on markets where agents have utility functions and commitments vary. Specifically, we analyze a dynamic matching game in which firms make offers to workers in each period, considering three types of commitment: (i) no commitment from either side, (ii) firms' commitment, and (iii) workers' commitment. Our results demonstrate that stable matchings can be supported as stationary equilibria under different commitment scenarios, depending on the strategies adopted by firms and workers. Furthermore, we identify key conditions, such as discount factors, that influence agents' decisions to switch partners, thereby shaping equilibrium outcomes. |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2411.19372 |
| By: | Hajdini, Ina; Knotek, Edward S; Leer, John; Pedemonte, Mathieu; Rich, Robert; Schoenle, Raphael |
| Abstract: | Using a large, nationally representative survey of US consumers, we estimate a causal 20 percent pass-through from inflation expectations to income growth expectations for the average consumer, with considerable heterogeneity in pass-through associated with sociodemographic factors. The results also indicate that higher inflation expectations cause an increase in consumers' likelihood to search for higher-paying jobs but do not change the likelihood of asking for a raise, suggesting that consumers recognize significant wage rigidity with their current employer. In a calibrated search-and-matching model, we find that demand and supply shocks combined with incomplete pass-through produce a strong negative relationship between expected inflation and expected utility. Taken together, the survey results and model analysis provide a labor market account of why people dislike inflation. |
| Keywords: | Inflation;Wage-price spiral;Expectations;randomized controlled trial |
| JEL: | E31 E24 E71 C83 |
| Date: | 2025–01 |
| URL: | https://d.repec.org/n?u=RePEc:idb:brikps:13937 |
| By: | Martin Browning; Laurens Cherchye; Demuynck Thomas; Bram De Rock; Frederic Vermeulen |
| Abstract: | We model the interaction between the marriage market and the intra household allocation of resources. We do this within a setting that accounts for both economic gains to marriage (through public consumption) and un observed non-material match quality, without relying on the transferable utility assumption. We adopt an axiomatic approach that leads to the em pirically tractable “Additive Quantity Shifting” (AQS) model. We develop a revealed preference methodology that is able to identify individuals’ het erogeneous match qualities and to quantify them in money metric terms. The methodology can include both preference factors, affecting individuals’ preferences over private and public goods, and match quality factors, driv ing differences in unobserved match quality. We demonstrate the practical usefulness of our methodology through an application to the Belgian MEqIn data. Our results reveal intuitive patterns of match quality that allow us to rationalise both the observed matches and the within-household allocations of time and money. |
| Date: | 2024 |
| URL: | https://d.repec.org/n?u=RePEc:ete:ceswps:746808 |
| By: | E. Emanuel Rapsch |
| Abstract: | A general theory of stochastic extensive forms is developed to bridge two concepts of information flow: decision trees and refined partitions on the one side, filtrations from probability theory on the other. Instead of the traditional "nature" agent, this framework uses a single lottery draw to select a tree of a given decision forest. Each "personal" agent receives dynamic updates from an own oracle on the lottery outcome and makes partition-refining choices adapted to this information. This theory addresses a key limitation of existing approaches in extensive form theory, which struggle to model continuous-time stochastic processes, such as Brownian motion, as outcomes of "nature" decision making. Additionally, a class of stochastic extensive forms based on time-indexed action paths is constructed, encompassing a wide range of models from the literature and laying the groundwork for an approximation theory for stochastic differential games in extensive form. |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2411.17587 |
| By: | Mario Ghossoub; Qinghua Ren; Ruodu Wang |
| Abstract: | We study risk sharing among agents with preferences modeled by heterogeneous distortion risk measures, who are not necessarily risk averse. Pareto optimality for agents using risk measures is often studied through the lens of inf-convolutions, because allocations that attain the inf-convolution are Pareto optimal, and the converse holds true under translation invariance. Our main focus is on groups of agents who exhibit varying levels of risk seeking. Under mild assumptions, we derive explicit solutions for the unconstrained inf-convolution and the counter-monotonic inf-convolution, which can be represented by a generalization of distortion risk measures. Furthermore, for a group of agents with different levels of risk aversion or risk seeking, we consider a portfolio manager's problem and explicitly determine the optimal investment strategies. Interestingly, we observe a counterintuitive phenomenon of comparative statics: even if all agents in the group become more risk seeking, the portfolio manager acting on behalf of the group may not necessarily allocate a larger proportion of investments to risky assets, which is in sharp contrast to the case of risk-averse agents. |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2412.00655 |
| By: | Roberto-Rafael Maura-Rivero; Chirag Nagpal; Roma Patel; Francesco Visin |
| Abstract: | Current methods that train large language models (LLMs) with reinforcement learning feedback, often resort to averaging outputs of multiple rewards functions during training. This overlooks crucial aspects of individual reward dimensions and inter-reward dependencies that can lead to sub-optimal outcomes in generations. In this work, we show how linear aggregation of rewards exhibits some vulnerabilities that can lead to undesired properties of generated text. We then propose a transformation of reward functions inspired by economic theory of utility functions (specifically Inada conditions), that enhances sensitivity to low reward values while diminishing sensitivity to already high values. We compare our approach to the existing baseline methods that linearly aggregate rewards and show how the Inada-inspired reward feedback is superior to traditional weighted averaging. We quantitatively and qualitatively analyse the difference in the methods, and see that models trained with Inada-transformations score as more helpful while being less harmful. |
| Date: | 2025–01 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2501.06248 |
| By: | Patrick Lahr; Axel Niemeyer |
| Abstract: | This paper characterizes extreme points of the set of incentive-compatible mechanisms for screening problems with linear utility. Extreme points are exhaustive mechanisms, meaning their menus cannot be scaled and translated to make additional feasibility constraints binding. In problems with one-dimensional types, extreme points admit a tractable description with a tight upper bound on their menu size. In problems with multi-dimensional types, every exhaustive mechanism can be transformed into an extreme point by applying an arbitrarily small perturbation. For mechanisms with a finite menu, this perturbation displaces the menu items into general position. Generic exhaustive mechanisms are extreme points with an uncountable menu. Similar results hold in applications to delegation, veto bargaining, and monopoly problems, where we consider mechanisms that are unique maximizers for specific classes of objective functionals. The proofs involve a novel connection between menus of extreme points and indecomposable convex bodies, first studied by Gale (1954). |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2412.00649 |
| By: | Papastaikoudis, I.; Prodromidis, P.; Watson, J.; Lestas, I. |
| Abstract: | We propose a new approach in public economics in a decentralized finance setting by using distributed optimization techniques for the planning of inter-regional and intra-regional public works/services for multiple regions each one with its own budget, natural and population characteristics. The goal of this study is to provide a toolkit for the planning of vast public works/services in an optimal way across the regions in order to improve the welfare of their respective populations. The proposed optimization approach can assist the government regarding its policy making for the public infrastructure, e.g., in the prioritization of the various public units across regions and also in the optimal geographical allocation of them. We will interpret the problem as a utility maximization problem and we will calculate the Marshallian demand for the public infrastructure. |
| Keywords: | Public Economics, Public Finance, Network Optimization |
| JEL: | C61 C62 D11 D30 D85 H40 H70 |
| Date: | 2025–01–22 |
| URL: | https://d.repec.org/n?u=RePEc:cam:camdae:2503 |
| By: | Rodrigo Jardim Raad (Cedeplar/UFMG); Aloísio Araújo (Cedeplar/UFMG) |
| Abstract: | Kubler and Schmedders (2005) showed that a competitive equilibrium can be far from an exact equilibrium when computed using first-order conditions. This paper shows that a competitive equilib- rium is implemented by recursive statistics with a minimal state space. This result allows us to develop an alternative method for computing the equilibrium without using first order conditions and smoothness assumptions. We compute the recursive equilibrium through a functional iteration algorithm and show that its implemented equilibrium allocation is arbitrarily close to an exact competitive equilibrium. In particular, we simulate some stochastic equilibrium processes in which agents anticipate exogenous un- certainty using some rules described in the literature of behavioral finance. An important stylized fact that is found suggests that incomplete markets favor agents with rational expectations when the expected asset return is high in relation to the risk-free asset. |
| Keywords: | Survival; Recursive Equilibrium; Ambiguity Aversion; Behavioral finance; Noise Traders; Incomplete Markets. |
| JEL: | D58 D52 |
| Date: | 2024–12 |
| URL: | https://d.repec.org/n?u=RePEc:cdp:texdis:td677 |
| By: | Mr. Bas B. Bakker |
| Abstract: | The economic literature has long attributed non-zero expected excess returns in currency markets to time-varying risk premiums demanded by risk-averse investors. This paper, building on Bacchetta and van Wincoop's (2021) portfolio balance framework, shows that such returns can also arise when investors are risk-neutral but face portfolio adjustment costs. Models with adjustment costs but no risk aversion predict a negative correlation between exchange rate levels and expected excess returns, while models with risk aversion but no adjustment costs predict a positive one. Using data from nine inflation targeting economies with floating exchange rates (2000–2024), we find strong empirical support for the adjustment costs framework. The negative correlation persists even during periods of low market stress, further evidence that portfolio adjustment costs, not risk premium shocks, drive the link between exchange rates and excess returns. Our model predicts that one-year expected excess returns should have predictive power for multi-year returns, with longer-term expected returns as increasing multiples of short-term expectations, and the predictive power strengthening with the horizon. We confirm these findings empirically. We also examine scenarios combining risk aversion and adjustment costs, showing that sufficiently high adjustment costs are essential to generate the observed negative relationship.These findings provide a simpler, testable alternative to literature relying on assumptions about unobservable factors like time-varying risk premiums, intermediary constraints, or noise trader activity. |
| Keywords: | Exchange Rates; Portfolio Balance; Uncovered Interest Parity; Portfolio Adjustment Costs; Risk Premium; Currency Markets; Expected Returns |
| Date: | 2025–01–17 |
| URL: | https://d.repec.org/n?u=RePEc:imf:imfwpa:2025/011 |
| By: | Qiqi Li; Wei Wang; Yiying Zhang |
| Abstract: | In economic analysis, rational decision-makers often take actions to reduce their risk exposure. These actions include purchasing market insurance and implementing prevention measures to modify the shape of the loss distribution. Under the assumption that the insureds' actions are fully observed by the insurer, this paper investigates the interaction between self-protection and insurance demand when insurance premiums are determined by convex premium principles within the framework of distortion risk measures. Specifically, the insured selects an optimal proportional insurance share and prevention effort to minimize the risk measure of their end-of-period exposure. We explicitly characterize the optimal combination of prevention effort and insurance demand in a self-protection model when the insured adopts tail value-at-risk and strictly convex distortion risk measures, respectively. Additionally, we conduct comparative static analyses to illustrate our main findings under various premium structures, risk aversion levels, and loss distributions. Our results indicate that market insurance and self-protection are complementary, supporting classical insights from the literature regarding corner insurance policies (i.e., null and full insurance) in the absence of ex ante moral hazard. Finally, we consider the effects of moral hazard on the interaction between self-protection and insurance demand. Our findings show that ex ante moral hazard shifts the complementary effect into substitution effect. |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2411.19436 |