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on Utility Models and Prospect Theory |
| By: | Emil Horobet |
| Abstract: | In this article, we study the generalized modern portfolio theory, with utility functions admitting higher-order cumulants. We establish that under certain genericity conditions, the utility function has a constant number of complex critical points. We study the discriminant locus of complex critical points with multiplicity. Finally, we switch our attention to the generalization of the feasible portfolio set (variety), determine its dimension, and give a formula for its degree. |
| Date: | 2025–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2511.20674 |
| By: | Zachary Van Oosten; Ruodu Wang |
| Abstract: | We distinguish two frameworks for decisions under ambiguity: evaluate-then-aggregate (ETA) and aggregate-then-evaluate (ATE). Given a statistic that represents the decision maker's pure-risk preferences (such as expected utility) and an ambiguous act, an ETA model first evaluates the act under each plausible probabilistic model using this statistic and then aggregates the resulting evaluations according to ambiguity attitudes. In contrast, an ATE model first aggregates ambiguity by assigning the act a single representative distribution and then evaluates that distribution using the statistic. These frameworks differ in the order in which risk and ambiguity are processed, and they coincide when there is no ambiguity. While most existing ambiguity models fall within the ETA framework, our study focuses on the ATE framework, which is conceptually just as compelling and has been relatively neglected in the literature. We develop a Choquet ATE model, which generalizes the Choquet expected utility model by allowing arbitrary pure-risk preferences. We provide an axiomatization of this model in a Savage setting with an exogenous source of unambiguous events. The Choquet ATE framework allows us to analyze a wide range of ambiguity attitudes and their interplay with risk attitudes. |
| Date: | 2025–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2512.03396 |
| By: | Zeyun Hu; Yang Liu |
| Abstract: | We investigate the static portfolio selection problem of S-shaped and non-concave utility maximization under first-order and second-order stochastic dominance (SD) constraints. In many S-shaped utility optimization problems, one should require a liquidation boundary to guarantee the existence of a finite concave envelope function. A first-order SD (FSD) constraint can replace this requirement and provide an alternative for risk management. We explicitly solve the optimal solution under a general S-shaped utility function with a first-order stochastic dominance constraint. However, the second-order SD (SSD) constrained problem under non-concave utilities is difficult to solve analytically due to the invalidity of Sion's maxmin theorem. For this sake, we propose a numerical algorithm to obtain a plausible and sub-optimal solution for general non-concave utilities. The key idea is to detect the poor performance region with respect to the SSD constraints, characterize its structure and modify the distribution on that region to obtain (sub-)optimality. A key financial insight is that the decision maker should follow the SD constraint on the poor performance scenario while conducting the unconstrained optimal strategy otherwise. We provide numerical experiments to show that our algorithm effectively finds a sub-optimal solution in many cases. Finally, we develop an algorithm-guided piecewise-neural-network framework to learn the solution of the SSD problem, which demonstrates accelerated convergence compared to standard neural network approaches. |
| Date: | 2025–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2512.00299 |
| By: | Albina Danilova; Valentin Lizhdvoy |
| Abstract: | This paper studies a Kyle-Back model with a risk-averse insider possessing exponential utility and a dynamic stochastic signal about the asset's terminal fundamental value. While the existing literature considers either risk-neutral insiders with dynamic signals or risk-averse insiders with static signals, we establish equilibrium when both features are present. Our approach imposes no restrictions on the magnitude of the risk aversion parameter, extending beyond previous work that requires sufficiently small risk aversion. We employ a weak conditioning methodology to construct a Schr\"{o}dinger bridge between the insider's signal and the asset price process, an approach that naturally accommodates stochastic signal evolution and removes risk aversion constraints. We derive necessary conditions for equilibrium, showing that the optimal insider strategy must be continuous with bounded variation. Under these conditions, we characterize the market-maker pricing rule and insider strategy that achieve equilibrium. We obtain explicit closed-form solutions for important cases including deterministic and quadratic signal volatilities, demonstrating the tractability of our framework. |
| Date: | 2025–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2512.05011 |
| By: | Alfred Galichon; Antoine Jacquet; Georgy Salakhutdinov |
| Abstract: | We present a general framework for matching with transferable utility (TU) that accommodates arbitrary heterogeneity without relying on the logit structure. The optimal assignment problem is characterized by tractable linear programming formulation, allowing flexible error distributions and correlation patterns. We introduce an iterative algorithm that solves large-scale assignment problems with guaranteed convergence and an intuitive economic interpretation, and we show how the same structure supports a simulated moment-matching estimator of the systematic surplus. Experiments using simulated data demonstrate the algorithm's scalability and the estimator's consistency under correct specification, as well as systematic bias arising from logit misspecification. |
| Date: | 2025–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2511.23116 |
| By: | James C. Cox; Cary Deck; Laura Razzolini; Vjollca Sadiraj |
| Abstract: | Deviations from choices predicted by self-regarding preferences have regularly been observed in standard dictator games. Such behavior is not inconsistent with conventional preference theory or revealed preference theory, which accommodate other-regarding preferences. By contrast, experiments in which giving nothing is not the least generous feasible act produce data that is inconsistent with conventional preference theory including social preference models and suggest the possible relevance of reference point models. Two such models are the reference-dependent theory of riskless choice with loss aversion and choice monotonicity in moral reference points. Our experiment includes novel treatments designed to challenge both theoretical models of reference dependence and conventional rational choice theory by poking holes in or adding to the dictator's feasible set along with changes to the initial endowment of the players. Our design creates tests that at most one of these models can pass. However, we do not find that any of these models fully capture behavior. In part this result is due to our observing behavior in some treatments that differs from previous experiments for reasons attributable to implementation differences across studies. |
| Keywords: | Rational Choice Theory, Reference Dependence, Behavioral Models, Laboratory Experiments |
| JEL: | C7 C9 D9 |
| Date: | 2025–11 |
| URL: | https://d.repec.org/n?u=RePEc:exc:wpaper:2025-02 |
| By: | Xie, Zoe Leiyu; Yu, Pei Cheng |
| Abstract: | his paper studies how the unemployment insurance system should be designed when considering costly self-control. The standard optimal unemployment insurance with dynamic moral hazard features declining benefits over the unemployment spell, without a lower bound on consumption (“immiseration”). As documented in the empirical literature, unemployed workers may be tempted to undervalue the future benefits of job search. The paper models this behavioral bias using costly self-control—a utility cost incurred when a worker’s job search choice deviates from the choice that maximizes current period utility and disregards future utility. Compared with the standard setup with moral hazard alone and without behavioral bias, the optimal system features lower benefit levels, a less rapid decline in benefits over the unemployment spell, a lower bound on consumption for the unemployed, and a one-time reward when a worker returns to work. The findings suggest that food assistance benefits and a back-to-work bonus in many U.S. states are broadly in line with such an optimal unemployment system. |
| Date: | 2025–12–01 |
| URL: | https://d.repec.org/n?u=RePEc:wbk:wbrwps:11265 |
| By: | Cheng Weilun; Liang Zongxia; Wang Sheng; Xia Jianming |
| Abstract: | This paper investigates infinite-dimensional portfolio selection problem under a general distribution of the risk aversion parameter. We provide a complete characterization of all deterministic equilibrium investment strategies. Our results reveal that the solution structure depends critically on the distribution of risk aversion: the equilibrium is unique whenever it exists in the case of finite expected risk aversion, whereas an infinite expectation can lead to infinitely many equilibria or to a unique trivial one (pi equals 0). To address this multiplicity, we introduce three optimality criteria-optimal, uniformly optimal, and uniformly strictly optimal-and explicitly characterize the existence and uniqueness of the corresponding equilibria. Under the same necessary and sufficient condition, the optimal and uniformly optimal equilibria exist uniquely and coincide. Furthermore, by additionally assuming that the market price of risk is non-zero near the terminal time, we show that the optimal (and hence uniformly optimal) equilibrium is also uniformly strictly optimal. Finally, we perform comparative statics to demonstrate that a risk aversion distribution dominating another in the reverse hazard rate order leads to a less aggressive equilibrium strategy. |
| Date: | 2025–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2512.00830 |
| By: | Moshe A. Milevsky; Thomas S. Salisbury; Robyn Allen |
| Abstract: | We investigate the extent to which groups with elevated mortality rates ex ante might opt out of guaranteed national pensions in favour of demographically aligned plans, which we label equitable longevity risk sharing (ELRiS) pools, even if this involves accepting some idiosyncratic risk. Technically, this paper develops a stochastic model of retirement income within an ELRiS structure that is calibrated to equate the discounted expected utility of a guaranteed national pension. The practical motivation for developing this alternative is that working members of First Nations peoples of Canada: (1) experience much higher mortality rates than average over their entire life cycle, and (2) some are actually allowed by current legislation to opt out of the Canada Pension Plan (CPP). We then demonstrate that under reasonable economic preferences and parameters, a sub-group with a 10-year life expectancy gap relative to the population could attain equivalent lifetime utility by contributing a mere two-thirds to the plan, even if they were pooled with only 30 members. For a longevity gap of 20 years, such as between an Indigenous male versus a non-Indigenous female, the contribution rate falls to less than a third. The difference between the statutory and mandatory contribution rates to a guaranteed national pension and those needed within these self-sustaining pools is an implicit subsidy from Indigenous to non-Indigenous. From a policy perspective, this paper aspires to jump-start a conversation that sparks a change in a status quo, which is obviously unfair and inequitable. |
| Date: | 2025–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2512.00122 |
| By: | Yao Wu |
| Abstract: | Conventional models of matching markets assume that monetary transfers can clear markets by compensating for utility differentials. However, empirical patterns show that such transfers often fail to close structural preference gaps. This paper introduces a market microstructure framework that models matching decisions as a limit order book system with rigid bid ask spreads. Individual preferences are represented by a latent preference state matrix, where the spread between an agent's internal ask price (the unconditional maximum) and the market's best bid (the reachable maximum) creates a structural liquidity constraint. We establish a Threshold Impossibility Theorem showing that linear compensation cannot close these spreads unless it induces a categorical identity shift. A dynamic discrete choice execution model further demonstrates that matches occur only when the market to book ratio crosses a time decaying liquidity threshold, analogous to order execution under inventory pressure. Numerical experiments validate persistent slippage, regional invariance of preference orderings, and high tier zero spread executions. The model provides a unified microstructure explanation for matching failures, compensation inefficiency, and post match regret in illiquid order driven environments. |
| Date: | 2025–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2511.20606 |