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on Utility Models and Prospect Theory |
| By: | Qi-Qing Song; Jia-Lin Liu; Jia-Yu Cui |
| Abstract: | This paper investigates the non-emptiness of the fuzzy core and introduces the notion of the TU-fuzzy core for pure exchange economies with discontinuous utility functions. We propose two stability conditions: local fuzzy-coalition stability and local TU-fuzzy-coalition stability. We also introduce an independent-$\pi$-balanced family of subsets of the agent set to construct two payoff-dependent NTU games. These constructions serve as bridges linking the fuzzy core, the TU-fuzzy core, and NTU games. Under the proposed stability conditions, we establish the non-emptiness of the fuzzy core for economies with quasi-concave utility functions and the non-emptiness of the TU-fuzzy core for economies with concave utility functions. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.06572 |
| By: | Endre Cs\'oka; M\'at\'e Viczi\'an |
| Abstract: | The Guaranteed Utility Mechanism (GUM) was introduced to implement efficiency in Guaranteed Utility Equilibrium (GUE) in dynamic social choice problems. We show that this mechanism also has a previously unknown connection to risk minimization. Fixing an efficient decision policy, we study variance-minimizing budget-balanced transfer rules in the class of GUE-implementations of truthful reporting. A symmetrized version of GUM (sym-GUM) minimizes the sum of the agents' utility variances under truthful reporting when there is no public state. When a public state is present, a slight modification of this rule yields the minimizer for the same objective. Sym-GUM, however, does not minimize transfer risk. The minimizer for that problem is instead the symmetrized version of a closely related GUM-like transfer rule. In both problems, the minimizing truthful total transfers are unique up to agent-specific constants summing to zero and events of probability zero. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.10456 |
| By: | G. Charles-Cadogan |
| Abstract: | The paper places the Samuelson--Merton ``util-prob'' construction and preference-based state-price interpretation inside a continuous-time equivalent-martingale-measure framework. The contribution is not the existence of a marginal-utility pricing kernel, but a compensated stochastic-exponential representation of the ``util-prob'' density. Behavioral weighting by marginal utility becomes an equivalent martingale measure only after the drift generated by risk aversion and prudence is compensated. Under positivity, integrability, normalization, and martingale conditions, the behavioral density is generated by the Brownian kernel $-A_t\sigma_t$, where $A_t$ is Arrow--Pratt risk attitude and $\sigma_t$ is state volatility. The required compensator identifies the finite-variation term that must be removed before marginal-utility weighting defines a true martingale density. The framework preserves put--call parity under a common admissible kernel and yields a Cox--Ross risk-premium identity linking option and underlying premia through volatility exposures. Empirically, the paper maps option-implied and physical densities into a signed Arrow--Pratt decomposition, with positive curvature interpreted as risk aversion and negative curvature as risk-seeking or speculative tilt. In a panel of liquid index ETF and single-name options, arbitrage-penalized EBMM has lower pooled holdout squared-error loss than arbitrage-penalized SVI when both models receive the same total-variance positivity and butterfly-density penalties, although slice-level results remain mixed. The exercise is best read as a density-ratio admissibility test rather than a replacement for production volatility-surface estimation. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.08803 |
| By: | Tim Wienand; Brice Magdalou; Richard Nock; Paul Hufe |
| Abstract: | We develop a framework to evaluate income distributions from the perspective of an opportunity-egalitarian social planner. Through an original axiomatic route that bridges normative economics and decision theory under ambiguity, we characterize a class of social welfare functions governed by a single parameter capturing the planner's aversion to inequality of opportunity. We obtain a `mean-divergence' representation that separates economic efficiency from a penalty for inequality of opportunity, as well as a stochastic dominance criterion for robust welfare comparisons. We apply these theoretical results to analyze opportunity-sensitive social welfare in the United States across birth cohorts and regions. Mapping standard estimates of intergenerational mobility into our framework, we show that welfare rankings vary substantially with the assumed degree of inequality-of-opportunity aversion. We transparently gauge the extent of this normative ambiguity by providing bounds on the ranking of birth cohorts and regions, respectively. |
| Keywords: | inequality of opportunity, intergenerational mobility, welfarism, utilitarianism, social welfare measurement |
| JEL: | D31 D63 I31 |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:ces:ceswps:_13034 |
| By: | Gechun Liang; Moris S. Strub; Yuwei Wang; Zhaojun Yang |
| Abstract: | We develop a framework for an investor who trades until she either reaches a financial goal or an exogenous deadline arrives. Analogous to utility functions over wealth, we measure satisfaction with the timing of reaching a goal by a discount function. For a continuous-time market where a stochastic factor drives the dynamics of stock prices and the financial goals, the investor maximizes the expected discount at the goal reaching time and the expected utility of the funding ratio if the goal remains unreached by the deadline. This setup leads to a new class of stochastic control problems. We establish Bellman's principle of optimality and characterize the value function as a viscosity solution to the associated Hamilton-Jacobi-Bellman equation. When the deadline is infinite and the goal is constant, the HJB equation reduces to a form related to the backward heat equation, for which we provide a complete characterization of smooth solutions. When analytical solutions are unavailable, we develop an approach based on Howard's algorithm to obtain numerical solutions. Our analysis shows that optimal investment policies for goal reaching problems can be decreasing in the drift of risky assets and need not converge to full risk-free investment even as volatility diverges to infinity. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.10046 |
| By: | Danilo Cavapozzi; Marco Francesconi; Cheti Nicoletti |
| Abstract: | Women perform most of the housework despite substantial convergence in labor market outcomes. We develop and estimate a semi-structural model of household housework decisions that combines randomized vignette experiments with an epidemiological identification strategy to estimate the contributions of economic utility and social norms. Equal sharing of housework yields higher economic utility for both men and women, while households use domestic work to offset differences in labor market involvement. Yet women continue to perform a disproportionate share of housework, largely because of social norms. Exposure to more egalitarian gender norms significantly increases the likelihood of more balanced housework allocations. |
| Keywords: | Intrahousehold allocation of chores, Labor supply, Vignettes, Gender role norms, Gender gaps |
| JEL: | C25 C26 D13 J16 J22 |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:crm:wpaper:26227 |
| By: | Julien Monardo; Mogens Fosgerau; Andr\'e de Palma |
| Abstract: | We introduce a class of demand models for market-level data. The models can be estimated by linear instrumental variables regression while accommodating substitution patterns far richer than the logit and nested logit models they embed. They are built from closed-form inverse market share functions through a generator analogous to McFadden's generalized extreme value generating function, but acting on market shares. Constructive results allow arbitrary nesting structures, including overlapping nests and partial membership, yielding inverse-share analogs of generalized extreme value models. The class is consistent with utility maximization and strictly larger than the class of regular additive random utility models. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.10069 |
| By: | Balazs Hoffmann; Miklos Rasonyi |
| Abstract: | We investigate a continuous-time financial market where the asset price exhibits weak (sublinear) mean reversion and has a nonzero drift. Complementing earlier work on strong (superlinear) mean reversion, we show that, for an investor maximizing expected exponential utility, the certainty equivalent grows as $O(T^{2\beta+1})$ where $0 |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.08631 |
| By: | Ram Sewak Dubey; Giorgio Laguzzi |
| Abstract: | We study the existence of real-valued social welfare functions (SWFs) on the set of infinite utility streams that satisfy anonymity and almost weak Pareto. We characterize the domains of one-period utilities, \(Y\subset \mathbb{R}\), for which such SWFs exist. We show that an SWF satisfying these two axioms exists if and only if \(Y\) contains no subset that is order-isomorphic to the set of negative and positive integers. Thus, the restrictions on \(Y\) required for the existence of an SWF satisfying anonymity and almost weak Pareto coincide with those required for an SWF satisfying anonymity and weak Pareto. Moreover, the SWF we construct is invariant under arbitrary permutations and satisfies stationarity, two properties that are particularly useful for decision making in infinite-horizon economies. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.05253 |
| By: | Andreas Kleiner |
| Abstract: | We study a model of delegation in which a principal takes a multidimensional action and an agent has private information about a multidimensional state. We provide necessary and sufficient conditions for an arbitrary mechanism to maximize the principal’s expected payoff. A key step shows that a function is the indirect utility of an incentive-compatible mechanism if and only if it is convex and lies below the agent’s full-discretion payoff. We apply our optimality conditions to convex delegation sets and characterize when a single budget optimally links decisions. Linking can preserve discretion even when separate dele gation would eliminate it. Optimal linking can also require a nonconvex delegation set, even with uniformly distributed types. If the principal cares little about aligned decisions, every optimal mechanism randomizes: risk in an aligned decision provides incentives in the biased ones at little cost to her. |
| Keywords: | delegation; mechanism design without transfers |
| JEL: | D82 D86 C61 |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2025_784 |
| By: | Zhaojie Ren; Sheng Wang; Tak Kwong Wong; Sheung Chi Phillip Yam |
| Abstract: | This article studies a retirement planning problem from a new perspective in which a retiree delegates an initial lump sum to a professional fund manager. The fund is managed dynamically to deliver lifelong benefits while satisfying a guarantee that, at all times, wealth remains above a prescribed solvency level and the benefit rate remains above a minimum level. We formulate this problem as a continuous-time stochastic control model, in which the controls are the benefit rate and the portfolio allocation, and the objective incorporates general utility functions over benefits, management fees, and terminal bequest. Conventional approaches such as standard viscosity solution and martingale methods are not immediately applicable here due to the simultaneous influence of (i) the control variable nature of the benefit rate; (ii) the guarantee constraints; and (iii) the running wealth-dependent utility. We develop a new approach that deals directly with the associated fully nonlinear Hamilton-Jacobi-Bellman equation and establish the unique existence of a classical solution. One particular trick for resolving this equation is to apply an intricate transform that diverts the former to a semilinear auxiliary equation. A major contribution is to establish the existence of the solution to the auxiliary equation and characterize its precise growth, derivative, and boundary behavior. These results are crucial for establishing the verification theorems and deriving the optimal strategy. Besides, numerical experiments indicate that guarantee constraints induce more conservative policies, particularly at low wealth levels, while providing effective downside protection for both wealth and benefits. The associated well-being loss relative to the unconstrained framework remains small, suggesting that incorporating guarantees into retirement products is practically appealing. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.06504 |
| By: | David Argente |
| Abstract: | Complementarities can have important welfare consequences, but quantifying these effects would seem to require identifying and valuing the underlying mechanisms separately. This paper shows that this need not be the case. I provide necessary and sufficient conditions under which baseline subsidized activity and the direct and total responses to a subsidy determine aggregate willingness to pay. A sufficient condition for valuing the equilibrium adjustment is that it has the same effect on utility as an additional subsidy common to all agents and relevant actions. The formula is easy to apply to existing estimates and guides the design of new experiments. |
| JEL: | D6 H2 H4 O2 |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:nbr:nberwo:35843 |
| By: | Sinan Ertemel |
| Abstract: | Weighted Shapley values represent asymmetry through positive weights and ordered priority classes. We give these parameters a preference interpretation in Roth's framework of lotteries over positions in transferable-utility games. Under common calibration, nullity, ordinary risk neutrality, unanimity efficiency, and unanimity positivity, position values in unanimity games are probability equivalents. Luce conditioning of these probabilities characterizes the Kalai-Samet family and is equivalent to partnership consistency. We separate conditioning into transitivity of revealed priority, pairwise determination of support, and invariance of positive odds. Two-player observations admit a weighted Shapley extension exactly when revealed priority is transitive and within-class odds satisfy a product rule. The extension is unique: pairwise comparisons identify the priority classes and weight ratios within each class. Larger unanimity games provide additional restrictions on supports and shares. We give constructive proofs, establish independence of the five axioms, and explain the scope and limits of the elicitation interpretation. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.09899 |