|
on Utility Models and Prospect Theory |
| By: | Ben Abramowitz |
| Abstract: | We examine formal games that we call "capital games" in which player payoffs are known, but their payoffs are not guaranteed to be von Neumann-Morgenstern utilities. In capital games, the dynamics of player payoffs determine their utility functions. Different players can have different payoff dynamics. We make no assumptions about where these dynamics come from, but implicitly assume that they come from the players' actions and interactions over time. We define an equilibrium concept called "growth equilibrium" and show a correspondence between the growth equilibria of capital games and the Nash equilibria of standard games. |
| Date: | 2025–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2510.00472 |
| By: | Yeshwanth Cherapanamjeri; Constantinos Daskalakis; Gabriele Farina; Sobhan Mohammadpour |
| Abstract: | Random Utility Models (RUMs) are a classical framework for modeling user preferences and play a key role in reward modeling for Reinforcement Learning from Human Feedback (RLHF). However, a crucial shortcoming of many of these techniques is the Independence of Irrelevant Alternatives (IIA) assumption, which collapses \emph{all} human preferences to a universal underlying utility function, yielding a coarse approximation of the range of human preferences. On the other hand, statistical and computational guarantees for models avoiding this assumption are scarce. In this paper, we investigate the statistical and computational challenges of learning a \emph{correlated} probit model, a fundamental RUM that avoids the IIA assumption. First, we establish that the classical data collection paradigm of pairwise preference data is \emph{fundamentally insufficient} to learn correlational information, explaining the lack of statistical and computational guarantees in this setting. Next, we demonstrate that \emph{best-of-three} preference data provably overcomes these shortcomings, and devise a statistically and computationally efficient estimator with near-optimal performance. These results highlight the benefits of higher-order preference data in learning correlated utilities, allowing for more fine-grained modeling of human preferences. Finally, we validate these theoretical guarantees on several real-world datasets, demonstrating improved personalization of human preferences. |
| Date: | 2025–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2510.15839 |
| By: | Yan Dolinsky |
| Abstract: | In this work we study a continuous time exponential utility maximization problem in the presence of a linear temporary price impact. More precisely, for the case where the risky asset is given by the Ornstein-Uhlenbeck diffusion process we compute the optimal portfolio strategy and the corresponding value. Our method of solution relies on duality, and it is purely probabilistic. |
| Date: | 2025–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2509.25472 |
| By: | Marielle Brunette; Stéphane Couture; Patrice Loisel |
| Abstract: | Decision-making processes increasingly involve ambiguity rather than risk, and multiple ambiguities rather than a single one. In this article, we consider how different sources of ambiguity, as well as two-source ambiguity, affect decision-making in relation to risk. We also examine the value of information that eliminates or reduces ambiguity. Finally, we analyse the effect of ambiguity preferences on the results. To this end, we propose an experiment in forest management in the context of climate change, which is a typical decision-making situation involving multiple ambiguities. We demonstrate that the various sources of ambiguity modify the optimal decision in comparison to situations involving risk. Furthermore, we demonstrate that ambiguity aversion significantly impacts the optimal decision. The results reveal that the value of information that eliminates one-source ambiguity is positive in both one- and two-source ambiguity situations. However, ambiguity aversion has no significant impact on this value. |
| Keywords: | risk, ambiguity, decision, information value |
| JEL: | D81 Q23 |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:ulp:sbbeta:2025-41 |
| By: | Xueying Huang; Peng Luo; Dejian Tian |
| Abstract: | This paper investigates an optimal consumption-investment problem featuring recursive utility via Tsallis relative entropy. We establish a fundamental connection between this optimization problem and a quadratic backward stochastic differential equation (BSDE), demonstrating that the value function is the value process of the solution to this BSDE. Utilizing advanced BSDE techniques, we derive a novel stochastic maximum principle that provides necessary conditions for both the optimal consumption process and terminal wealth. Furthermore, we prove the existence of optimal strategy and analyze the coupled forward-backward system arising from the optimization problem. |
| Date: | 2025–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2509.20888 |
| By: | Komatsubara, Takashi |
| Abstract: | This paper investigates whether sports experience changes adolescents’ preferences. For this purpose, we conducted a survey of Japanese university students about their sports experiences, time preferences, and risk aversion. Our regression analysis shows that students’ sports experience does not significantly change their time preferences or risk aversion. This result implies that although students devote a lot of time to sports in Japan, sports still do not have a significant impact on students’ attitudes towards time and risk. |
| Keywords: | Sports Experience, Time Preferences, Risk Aversion, Student Survey |
| JEL: | D81 I21 |
| Date: | 2025–09–01 |
| URL: | https://d.repec.org/n?u=RePEc:pra:mprapa:126001 |
| By: | Daniel Cunha Oliveira; Grover Guzman; Nick Firoozye |
| Abstract: | Robust optimization provides a principled framework for decision-making under uncertainty, with broad applications in finance, engineering, and operations research. In portfolio optimization, uncertainty in expected returns and covariances demands methods that mitigate estimation error, parameter instability, and model misspecification. Traditional approaches, including parametric, bootstrap-based, and Bayesian methods, enhance stability by relying on confidence intervals or probabilistic priors but often impose restrictive assumptions. This study introduces a non-parametric bootstrap framework for robust optimization in financial decision-making. By resampling empirical data, the framework constructs flexible, data-driven confidence intervals without assuming specific distributional forms, thus capturing uncertainty in statistical estimates, model parameters, and utility functions. Treating utility as a random variable enables percentile-based optimization, naturally suited for risk-sensitive and worst-case decision-making. The approach aligns with recent advances in robust optimization, reinforcement learning, and risk-aware control, offering a unified perspective on robustness and generalization. Empirically, the framework mitigates overfitting and selection bias in trading strategy optimization and improves generalization in portfolio allocation. Results across portfolio and time-series momentum experiments demonstrate that the proposed method delivers smoother, more stable out-of-sample performance, offering a practical, distribution-free alternative to traditional robust optimization methods. |
| Date: | 2025–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2510.12725 |
| By: | Andrew Li; R. Ravi; Karan Singh; Zihong Yi; Weizhong Zhang |
| Abstract: | Motivated by the problem of selling large, proprietary data, we consider an information pricing problem proposed by Bergemann et al. that involves a decision-making buyer and a monopolistic seller. The seller has access to the underlying state of the world that determines the utility of the various actions the buyer may take. Since the buyer gains greater utility through better decisions resulting from more accurate assessments of the state, the seller can therefore promise the buyer supplemental information at a price. To contend with the fact that the seller may not be perfectly informed about the buyer's private preferences (or utility), we frame the problem of designing a data product as one where the seller designs a revenue-maximizing menu of statistical experiments. Prior work by Cai et al. showed that an optimal menu can be found in time polynomial in the state space, whereas we observe that the state space is naturally exponential in the dimension of the data. We propose an algorithm which, given only sampling access to the state space, provably generates a near-optimal menu with a number of samples independent of the state space. We then analyze a special case of high-dimensional Gaussian data, showing that (a) it suffices to consider scalar Gaussian experiments, (b) the optimal menu of such experiments can be found efficiently via a semidefinite program, and (c) full surplus extraction occurs if and only if a natural separation condition holds on the set of potential preferences of the buyer. |
| Date: | 2025–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2510.15214 |
| By: | Alejandro Francetich; Burkhard C. Schipper (Department of Economics, University of California Davis) |
| Abstract: | We consider a principal who wishes to screen an agent with \emph{discrete} types by offering a menu of \emph{discrete} quantities and \emph{discrete} transfers. We assume that the principal's valuation is discrete strictly concave and use a discrete first-order approach. We model the agent's cost types as non-integer, with integer types as a limit case. Our modeling of cost types allows us to replicate the typical constraint-simplification results and thus to emulate the well-treaded steps of screening under a continuum of contracts. We show that the solutions to the discrete F.O.C.s need not be unique \textit{even under discrete strict concavity}, but we also show that there cannot be more than two optimal contract quantities for each type, and that---if there are two---they must be adjacent. Moreover, we can only ensure weak monotonicity of the quantities \textit{even if virtual costs are strictly monotone}, unless we limit the ``degree of concavity'' of the principal's utility. Our discrete screening approach facilitates the use of rationalizability to solve the screening problem. We introduce a rationalizability notion featuring robustness with respect to an open set of beliefs over types called \textit{$\Delta$-O Rationalizability}, and show that the set of $\Delta$-O rationalizable menus coincides with the set of usual optimal contracts---possibly augmented to include irrelevant contracts. |
| Keywords: | Screening, discrete concave optimization, rationalizability, level-$k$ reasoning |
| JEL: | D82 |
| Date: | 2025–10–23 |
| URL: | https://d.repec.org/n?u=RePEc:cda:wpaper:375 |
| By: | Gregorio Curello; Ludvig Sinander; Mark Whitmeyer |
| Abstract: | We uncover a close link between outside options and risk attitude: when a decision-maker gains access to an outside option, her behaviour becomes less risk-averse, and conversely, any observed decrease of risk-aversion can be explained by an outside option having been made available. We characterise the comparative statics of risk-aversion, delineating how effective risk attitude (i.e. actual choice among risky prospects) varies with the outside option and with the decision-maker's 'true' risk attitude. We prove that outside options are special: among transformations of a decision problem, those that amount to adding an outside option are the only ones that always reduce risk-aversion. |
| Date: | 2025–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2509.14732 |
| By: | Masaaki Fujii (Faculty of Economics, The University of Tokyo) |
| Abstract: | In this work, we combine the mean-field game theory with the classical idea of binomial tree framework, pioneered by Sharpe and Cox, Ross & Rubinstein, to solve the equilibrium price formation problem for the stock. For agents with exponential utilities and recursive utilities of exponential type, we prove the existence of a unique mean-field equilibrium and derive an explicit formula for equilibrium transition probabilities of the stock price by restricting its trajectories onto a binomial tree. The agents are subject to stochastic terminal liabilities and incremental endowments, both of which are dependent on unhedgeable common and idiosyncratic factors, in addition to the stock price path. Finally, we provide numerical examples to illustrate the qualitative effects of these components on the equilibrium price distribution. |
| Date: | 2025–10 |
| URL: | https://d.repec.org/n?u=RePEc:tky:fseres:2025cf1261 |
| By: | Ernst Fehr; Julien Senn; Thomas Epper; Aljosha Henkel |
| Abstract: | In this registered report, we investigate (i) whether incentives affect subjects’ willingness to pay to increase, and to decrease the payoff of others, (ii) whether they affect the distribution of social preference types, and (iii) whether they affect the strength and the precision of individuals’ structurally estimated social preference parameters. Using an online experiment with a general population sample, we show that the use of monetary incentives, as well as the size of the stakes, have little impact on subjects’ modal choices (descriptive analysis), as well as for the distribution of qualitatively distinct preference types in the population (clustering analysis). However, monetary incentives affect quantitative measures of the strength and the precision of social preferences. Indeed, a structural analysis reveals that the preference elicitation with merely hypothetical stakes leads to an overestimation and a less precise measurement of social preferences. Together, these results highlight that incentivizing the elicitation of social preferences is most useful when interested in quantitative estimates. For researchers interested in identifying merely qualitative preferences types, however, hypothetical stakes might suffice. |
| Keywords: | Social preferences, altruism, inequality aversion, incentives |
| JEL: | C80 C90 D30 D63 |
| Date: | 2025–10 |
| URL: | https://d.repec.org/n?u=RePEc:zur:econwp:482 |
| By: | Shuping Shi (Department of Economics, Macquarie University); Jun Yu (Faculty of Business Administration, University of Macau); Chen Zhang (Department of Economics, Sun Yat-sen University) |
| Abstract: | Forecasting realized volatility (RV) is central to financial econometrics, with important implications for risk management, asset allocation, and derivative pricing. Motivated by the ongoing debate on volatility modeling, this paper provides a comprehensive empirical comparison of many alternative models. We evaluate leading continuous time models estimated using state-of-the-art methods from the rough volatility literature, together with both standard long-memory autoregressive fractionally integrated moving average (ARFIMA) models and their rough-volatility extensions, as well as several variants of the heterogeneous autoregressive (HAR) model and their logarithmic counterparts. The models are applied to a large panel of equities and cryptocurrencies, with performance assessed using both statistical and economic criteria. Our results show that for equities, continuous time models consistently outperform discrete time alternatives across all evaluation criteria and forecasting horizons. The fractional Brownian motion model for log RV performs best at short horizons, while the fractional Ornstein Uhlenbeck model for log RV dominates in the long run. For cryptocurrencies, a mild divergence emerges between economic and statistical performance: based on realized utility, the quarticity-augmented heterogeneous autoregressive (HARQ) model for RV leads in the short term and the Brownian semistationary models prevail at longer horizons, whereas the HAR-type models for log RV deliver superior statistical accuracy. |
| Keywords: | Realized volatility, Continuous-time models, Discrete-time models, forecasting, economic utility |
| Date: | 2025–10 |
| URL: | https://d.repec.org/n?u=RePEc:boa:wpaper:202537 |
| By: | Peng Xu |
| Abstract: | This paper develops stochastic optimization problems for describing and analyzing behavioral investors with Markowitz Stochastic Dominance (MSD) preferences. Specifically, we establish dominance conditions in a discrete state-space to capture all reverse S-shaped MSD preferences as well as all subjective decision weights generated by inverse S-shaped probability weighting functions. We demonstrate that these dominance conditions can be admitted as linear constraints into the stochastic optimization problems to formulate computationally tractable mixed-integer linear programming (MILP) models. We then employ the developed MILP models in financial portfolio analysis and examine classic behavioral factors such as reference point and subjective probability distortion in behavioral investors' portfolio decisions. |
| Date: | 2025–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2509.22896 |
| By: | Fernández-Huertas Moraga, Jesús (Universidad Carlos III de Madrid) |
| Abstract: | International migrants choose their country of residence to maximize their utility. As a result, their choices are informative about the relative attractiveness of countries. This paper explains why Spain became the fourth most attractive country in the world for international migrants in the period 2015-2024, what I define as the Second Spanish Immigration Boom of the century. First, an accounting decomposition shows how, contrary to other destinations, Spanish-specific factors, correlated with economic conditions and general migration policies, have a larger weight in explaining immigration to Spain than origin-specific factors. Second, the causal relevance of bilateral visa policies is also shown, particularly in the context of Latin American immigrants, by using origins that are required a visa to enter Spain as a control for visa-free access countries in a generalized differences-in-differences setting. Finally, the effects of the Boom on immigrant selection are also analyzed, finding that the Second Boom was different from the first because educational selection improved. |
| Keywords: | gravity model, international migration, selection |
| JEL: | F22 J11 J61 O15 |
| Date: | 2025–10 |
| URL: | https://d.repec.org/n?u=RePEc:iza:izadps:dp18185 |