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on Utility Models and Prospect Theory |
| By: | Symeon Vaidanis; Marios Kountouris |
| Abstract: | This paper develops a binary-gamble framework for characterizing risk sensitivity and loss aversion in Cumulative Prospect Theory (CPT). The proposed probabilistic risk-sensitivity metric is defined as a probability-threshold ratio that determines acceptance and preference thresholds in choice problems involving either a certain outcome and a binary gamble or two binary gambles. We show how standard notions of symmetric and non-symmetric bet aversion can be recovered within this framework, and we compare the resulting threshold-based conditions with utility premia, probability premia, and Arrow--Pratt curvature measures. The analysis clarifies when these criteria coincide and when they diverge, particularly for increasing aversion conditions, binary gambles with unequal probability distributions, and settings involving probability weighting functions. We also identify technical restrictions that arise when CPT-utility functions are used to represent loss aversion at the reference point. The resulting framework provides a decision-theoretic interpretation of risk sensitivity that is directly tied to probability thresholds and complements existing premium-based approaches. |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2606.06652 |
| By: | Erhan Bayraktar; Emmet Lawless |
| Abstract: | We study an infinite-horizon optimal consumption-investment problem for an investor with Epstein-Zin stochastic differential utility with stochastic investment opportunities in an incomplete market. Risk aversion and intertemporal substitution are separated, and we work in the regime $\theta\in(0, 1)$, where there exists a unique generalised utility process for arbitrary non-negative progressively measurable consumption streams. Our main contribution is a variational characterisation of the value function. We show that the value function is the unique minimiser of a functional whose Euler-Lagrange equation coincides with the Hamilton-Jacobi-Bellman equation. Although the functional may be non-convex, the direct method yields existence, and we prove every minimiser is strictly positive, bounded, and classical. A verification theorem identifies any minimiser with the value function and gives feedback representations for optimal consumption and investment policies. The proof combines a change of measure to the myopic probability with uniqueness results for Epstein-Zin BSDEs and a perturbation argument for optimality. Examples with stochastic volatility, Gaussian excess returns, and fat-tailed excess returns illustrate the scope of the framework and its implications for intertemporal hedging. |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2606.02945 |
| By: | Piotr Frydrych |
| Abstract: | Worker utility is not observed -- only its consequence is. Each gig transaction produces a single bit: accepted or rejected. We argue this structure points directly to the Preisach hysteresis model as the natural representation of latent worker preferences. The Preisach operator models aggregate output as an integral over a population of binary threshold elements -- precisely the structure that emerges when heterogeneous workers each carry a private acceptance wage. We estimate two latent utility surfaces: acceptance utility U_1(X) and rejection utility U_0(X), via a dual-output neural network (shared layers 256->128, margin loss enforcing U_1 >= U_0). Classification reduces to the Preisach gap U_1(X) - U_0(X), passed into an XGBoost classifier alongside clip-stabilised price-to-threshold encodings. On 36, 891 gig transactions, this pipeline achieves Jaccard = 0.827 and ROC AUC = 0.799. The price-to-threshold encoding accounts for +11.0 pp AUC over raw utility features. The model confirms the directional asymmetry hysteresis predicts: price decreases depress completion rates more than equivalent increases raise them. Applied to the full dataset, the model's recommendations simultaneously reduce the total wage bill by 21.3% and increase expected fill rate by 9.7 pp. For 74.2% of transactions, P(accept) already exceeds 0.80; reducing the wage keeps it above threshold (mean post-cut P = 0.972), releasing cost savings (median 31%). For the remaining 25.4%, a median 7% wage increase recovers +43 pp acceptance. A model without an explicit indifference zone cannot execute both moves simultaneously. |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2606.04916 |
| By: | Sekimonyo, Jo M.; Casimir, Tara |
| Abstract: | This paper challenges the continued reliance on preference-based rational choice as the foundation of economic analysis. Traditional models assume that individuals continuously rank alternatives and act to maximize utility, yet a substantial body of empirical and experimental evidence shows behavior marked by inertia, impulsivity, and context dependence. Building on, but moving beyond, bounded rationality and prospect theory, this paper proposes Indifference Theory, grounded in a Propensity to Act (Pa) framework, as an alternative foundation for modeling action. The model reconceptualizes decision-making as threshold-based rational minimization of indifference. Individuals remain inactive when the margin of action, or indifference margin, is non-negative (Pa ≥ 0) and act only when it becomes negative (Pa |
| Keywords: | Indifference theory Propensity to act Behavioral economics Threshold models Decision-making Inertia Rational choice |
| JEL: | B5 D2 E2 H0 O3 |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:pra:mprapa:128992 |
| By: | Mateus Joffily (CNRS, Université Lumière Lyon 2, Université Jean Monnet Saint-Etienne, emlyon business school, GATE, 69007 Lyon, France); Thijs van de Laar (Department of Electrical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands) |
| Abstract: | Decision-makers exhibit well-defined yet distinct preference patterns under risk: a fourfold pattern when evaluating risky prospects, and a twofold pattern when making choices involving those same prospects. They also display loss aversion by rejecting mixed prospects with equivalent gains and losses, and a framing effect by reversing preferences when equivalent prospects are framed as gains or losses. We show that these phenomena - the fourfold and twofold patterns, loss aversion, and framing effect - arise naturally from a single hierarchical Bayesian framework. Crucially, this framework relies solely on prior beliefs about outcome probabilities and motivated beliefs about outcomes, without requiring probability weighting or reference-dependent value functions. |
| Keywords: | Fourfold Pattern; Probability Weighting; Bayesian Modeling |
| JEL: | C63 D81 D91 |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:gat:wpaper:2606 |
| By: | Anna Vakarova |
| Abstract: | I provide a unified framework to establish the existence of a weak Pareto efficient, envy-free allocation in general settings: random allocations are probability measures on a compact metric space, and preferences of agents are represented by continuous, concave utility function on the space of probability measures. The generality of my setting nests the existence results for small spaces with indivisibles -- the list of prominent applications includes the school assignment problem and the house allocation problem. The technique developed to prove the existence also applies to allocation problems with divisibles, like fair cake-cutting or land-division problems. Here I also show that even when agents' preferences are not atomless, the allocation in question can be represented as a probability measure over partitions with finite support. Last but not least, I apply the existence result to new allocation problems that no existing framework encompasses. These include allocation of indivisible goods or services over time and allocation of differentiated goods. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.28263 |
| By: | Appelbaum, Elie |
| Abstract: | This paper develops a theoretical model of decision-making under risk in which the agent is a union of individuals with heterogeneous attitudes toward risk. The risk attitude governing the joint decision is endogenously determined as a compromise between individuals' innate preferences, with deviations generating costs. The chosen risk attitude affects the optimal portfolio and, therefore, the risk premium associated with exposure to uncertainty. The analysis shows that the optimal compromise equates the marginal increase in the risk premium with the marginal reduction in deviation costs. Because risk attitudes and portfolio choices are jointly determined, parameter changes affect both sides of this condition, generating feedback effects that may lead to ambiguous or non-monotone comparative statics. The framework provides a tractable approach to modelling endogenous risk attitudes in collective decision-making under uncertainty. |
| Keywords: | household portfolio choice; heterogeneous risk preferences; Endogenous risk attitudes; collective decision making; preference aggregation. |
| JEL: | C18 C44 D80 D81 I10 |
| Date: | 2026–04 |
| URL: | https://d.repec.org/n?u=RePEc:pra:mprapa:129118 |
| By: | Ilia Shilov; Heinrich H. Nax; Saverio Bolognani |
| Abstract: | The Price of Anarchy (PoA) is a popular measure of the costs of decentralization in terms of efficiency losses. Almost all PoA analyses operate within a framework assuming both Cardinal Full-Comparability (CFC) and smoothness, in which case any derived bounds conveniently extend beyond pure Nash to coarse correlated equilibria and no-regret learning outcomes. However, interpersonal utility comparability is an additional assumption that generally has to be justified. Without it, cardinal utilities (e.g. defined under classical von Neumann--Morgenstern framework) are unique only up to agent-specific affine transformations, rendering both the utilitarian PoA and the classical smoothness conditions representation-dependent. In this paper, we operate under a more general Cardinal Non-Comparability (CNC) framework, under which the weighted Nash welfare is a canonical admissible aggregator. We introduce multiplicative smoothness, a product-form condition matched to the multiplicative structure of Nash welfare, and obtain PoA bounds that are CNC-invariant and extend to coarse correlated equilibria. We demonstrate applicability of our framework on single-choice welfare games, deriving the bounds through simple proof relying on multiplicative retention envelope and geometric closure. The interpretation of this bound in terms of the true cost of decentralization depends crucially on interpersonal comparability of utilities. |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2606.11397 |
| By: | Akay, Alpaslan (University of Gothenburg); Kartal, Nur (Turkish-German University) |
| Abstract: | Individuals’ time preferences may shape how they respond to increases in the income of comparable others. We argue that others’ higher income generates stronger disutility among impatient individuals, who seek immediate gratification, whereas patient individuals may experience lower disutility, or even utility, if they view income gaps as informative signals for future income growth and catching up. Using long-run panel data from the Socio-Economic Panel (SOEP), we examine whether patience moderates the relationship between relative income and life satisfaction. Fixed effects interaction models provide consistent evidence that the well-known disutility from relative income, often interpreted as a status effect, is mainly concentrated among impatient individuals with higher discount rates. By contrast, patient individuals, characterized by lower discount rates, stronger self-control, and better regulation of stress and anxiety, experience weaker disutility or even positive utility from others’ income, consistent with an information effect. The findings are robust to alternative income measures, savings, reference groups, and incentivised measures of time preferences. We discuss implications for behavioural and welfare economics |
| Keywords: | time-preferences, patience, life satisfaction, relative income, information effect |
| JEL: | C90 D63 |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:iza:izadps:dp18667 |
| By: | Sung Je Byun; Johnathan Loudis; Lawrence D.W. Schmidt |
| Abstract: | We construct a Broad Market Factor (BMF), which is a proxy for the value-weighted equity return on all firms in the US economy (public and private). The BMF differs from the standard Value-weighted Market Factor (VMF), which reflects the value-weighted equity return on public firms. We define the difference between the VMF and the BMF to be the Idiosyncratic Financial Factor (IFF). The IFF carries no risk premium and is uncorrelated with all macroeconomic proxies for investor marginal utility we consider. CAPM betas and, consequently, discount rates are underestimated when measured with respect to the VMF compared to the BMF for most portfolios. Size factors become redundant and the size anomaly is resolved when the VMF is replaced by the BMF in standard factor models. The intertemporal risk-return relation is substantially stronger when one replaces the VMF with the BMF. The unifying explanation for these results is that the IFF adds unpriced risk to the VMF, distorting both cross-sectional and time-series estimates of exposure to priced market risk. |
| JEL: | C15 C58 G12 G17 |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:nbr:nberwo:35243 |
| By: | Jake J. Xia |
| Abstract: | This paper develops a general framework for analyzing multi-agent systems with feedback loops between agents actions and collective observations. The framework is built on two fundamental agent-level variables: power, which measures agent influence on collective outcomes, and response functions, which determine how agents react to observations. We derive how macroscopic properties, including total power, useful power, entropy, order, fragility, and mobility, emerge from these two variables of heterogeneous agents. To study the trade off between growth and resilience, we introduce a system-level utility function parameterized by a risk-appetite coefficient and derive an optimal degree of order that balances productivity, stability, and adaptability. The analysis suggests that stronger synchronization can increase collective output but may also increase systemic fragility and reduce mobility. We further argue that order, entropy, information, and useful energy are task-dependent and system-relative concepts whose meanings depend on the objectives of the system. By measuring and designing agent power distributions and response functions, it may be possible to better understand, predict, and optimize collective behavior and identify the conditions under which collective intelligence and optimal order emerge. |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2606.20485 |
| By: | Rommin Adl; Peyton Williams |
| Abstract: | What happens when the strongest alliance member pressures a weaker member over territory and strategic control? We examine the Greenland sovereignty crisis as a stress test for LLM geopolitics, centered on the 2019-2026 U.S. push to acquire Greenland from the Kingdom of Denmark. The crisis nests two collective-action problems: Arctic strategic control and whether NATO can enforce alliance norms against the dominant member. We develop three games (asymmetric coercion; a NATO assurance game with a critical-mass tipping point; a triadic extensive-form game with social preferences) and test them with a multi-agent simulation in which eight frontier LLMs play six geopolitical roles (United States, Denmark, Greenland, NATO, Russia, Canada) across 3, 604 completed games and 108, 120 action observations. Using inverse game theory, we recover each model's structural utility parameters (alpha, beta, gamma, delta, eta) for material self-interest, reciprocity, inequality aversion, norm respect, and commitment consistency. Three findings stand out. First, all eight models become more escalatory under coercion framing (four-action escalation rises from 10.7% to 28.6%). Second, Chinese-origin models show systematically different power-weight profiles from Western-origin models when playing the U.S. role. Third, peaceful US acquisition emerges in only 1.9% of clean games and only 3 of 8 frontier models ever achieve it, most prominently DeepSeek V3.2, which executes a stable five-round playbook through the metropole. Prompts emphasizing jus cogens and self-determination reduce escalation back near baseline in the English-only confirmatory sample; multilingual contrasts are reported as exploratory sensitivity checks. We position this as a structural benchmark for LLM geopolitical behavior, complementing action-frequency benchmarks. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.22841 |
| By: | Pritchett, Lant; Viarengo, Martina |
| Abstract: | The first of the United Nations 2015 Sustainable Development Goals is: “End poverty in all its forms everywhere.” An implication of this broad goal is the existence of an array of poverty lines, which raises the question of an appropriate lower-bound and an upper-bound to global poverty lines. The ‘dollar-a-day’ poverty line (updated for inflation to P$2.15 in 2017 PPP) is widely accepted as a global lower-bound poverty line (GLBPL). However, while different countries, organizations, and authors use higher poverty lines, there is no consensus on a global upper bound poverty line (GUBPL). We estimate a GUBPL using two conceptually distinct approaches, both grounded in the tension between the focus axiom for poverty measures and standard economic social welfare measures. We set a candidate GUBPL either at: (i) the consumption consistent with the achievement of adequate material well-being or (ii) the consumption level where marginal utility is “near enough” zero. Using either approach, empirical results across an array of measures of well-being demonstrate that ad hoc poverty lines, including the World Bank's highest reported poverty line of P$6.85, are far too low to be plausible candidates for a GUBPL. Using the two approaches across four distinct indicators of well-being all of the empirical results suggest a GUBPL of at least P$21.5, ten times higher than the standard GLPBL of P$2.15. The use of both a lower bound and upper bound global poverty line balances the radically exclusive nature of the ‘dollar-a-day’ standard, which classifies people with very low levels of material well-being and hence very high marginal utility of income as “not poor” with an equally radically inclusive GUBPL which counts only those with globally high material achievement and low (ish) marginal utility of income as “not poor.” |
| Keywords: | poverty measurement; global poverty; welfare economics |
| JEL: | I32 D63 |
| Date: | 2026–06–30 |
| URL: | https://d.repec.org/n?u=RePEc:ehl:lserod:138336 |
| By: | Ronen Gradwohl; Fengming Hu; Rann Smorodinsky |
| Abstract: | We study the robustness of Bayesian persuasion to uncertainty about the receiver's preferences. We analyze two conceptually distinct notions: continuity, in which only the modeler lacks precise knowledge, but where the model's predictions are nonetheless accurate; and robustness, in which the sender also lacks precise knowledge, but where the outcome is insensitive to this ignorance. We model preference uncertainty as infinitesimally small, non-probabilistic (Knightian) uncertainty, and the sender's behavior as either minimizing the regret or maximizing the minimum utility. We show that continuity holds if and only if robustness holds, and that both notions are generic. Thus, while some instances of Bayesian persuasion are fragile, typical instances are both continuous and robust with respect to a small amount of ignorance. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.28265 |
| By: | Jingyuan Li; Ilia Tsetlin; Fan Wang |
| Abstract: | We present a Lean 4/Mathlib formalization of the additive representation theory behind Classical Lottery in Action and the Wakker-Debreu-Koopmans (WDK) layer it relies on. Our central result is a machine-checked proof that the cross-pair Thomsen / double-cancellation (hexagon) condition is irreducible from the ordinal axioms of additive conjoint measurement (weak order, restricted solvability, Archimedean condition, and tradeoff consistency). We exhibit an explicit verified counter-model (additiveRealBoolPref) satisfying all ordinal axioms yet failing the cross-pair condition, with every strict standard sequence being an arithmetic progression and hence non-dense. Around this boundary we mechanize the full derivable construction: continuous Debreu/Eilenberg utility from separability, standard-sequence grids, bisection methods from connectedness, and global additive gluing. All public theorems are sorry-free conditional wrappers over this single irreducible structural input. The development is kernel-clean, depending only on standard Lean foundations (propext, Classical.choice, Quot.sound). The companion file ClassicalLotteryInAction.lean formalizes local classical-lottery constructions, average-utility results, matching-frequency lemmas, and ambiguity-attitude statements used by the Management Science paper. This draws a precise, machine-certified line between what additive conjoint measurement can prove and what it must assume. |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2606.08902 |
| By: | María Florencia Gabrielli (Universidad del Desarrollo); Marcos Vergara (Universidad del Desarrollo) |
| Abstract: | We study the impact of risk aversion and cash flow risk on the allocation of equity shares between entrepreneurs and venture capitalists in a setting characterized by double-sided moral hazard. Cash flows are simultaneously influenced by both price risk and background risk. We evaluate the main results of the model through simulation exercises that highlight the parameters that influence the dynamics of optimal equity share in project cash ows, such as the entrepreneur's risk aversion relative to the VC's and other partner attributes like the productivity and efficiency of their respective efforts. We carried out the analysis under different risk and effort complementarity scenarios. We find that the productivity and efficiency of partners' efforts are dominated by their risk aversion, and that the slope of the effect of these traits on the optimal equity share trajectory is modi ed by risk parameters and effort complementarity. |
| Keywords: | Risk aversion, risk, equity share, financial contracting |
| JEL: | D81 D86 L26 |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:aoz:wpaper:398 |
| By: | abe housh, Najm |
| Abstract: | Decision biases are commonly interpreted as systematic deviations from rational evaluation, arising from distorted preferences, heuristics, or computational limitations. This article challenges that assumption by proposing that many biases are not errors, but outcomes of a structured process of evaluative selection operating under constraint. Within this framework, decision-making is modeled as a dynamic process in which alternatives are evaluated through the interaction of symbolic value, functional return, and constraint structures, modulated by context-sensitive reweighting. Crucially, evaluation does not operate over a fixed set of representations. Instead, the evaluative field is selectively constructed through memory activation, such that only a subset of representations becomes available for comparison at any given moment. Biases are therefore redefined as selection outcomes produced under asymmetric weighting and constrained evaluative access. This account explains why behavioral regularities such as loss aversion, present bias, cognitive dissonance, and status quo preference can appear both stable and context-dependent, without invoking systematic irrationality. The article further develops the empirical implications of this framework by proposing experimental designs that manipulate not only outcome structure but also representational access and weighting conditions. It predicts that biases can be attenuated, amplified, or reversed through controlled variation in memory activation, contextual framing, and threshold conditions governing selection. By shifting the focus from deviation to structure, the framework provides a unified account linking conceptual analysis, decision dynamics, and experimental design, offering a foundation for a selection-based theory of decision-making. |
| Keywords: | Decision Biases Evaluative Selection Dynamic Reweighting Memory Activation Bounded Rationality Behavioral Economics Loss Aversion Present Bias Status Quo Bias Cognitive Dissonance Symbolic-Functional Framework Decision Making Dynamics Experimental Design |
| JEL: | B41 C91 D03 D83 |
| Date: | 2026–04–16 |
| URL: | https://d.repec.org/n?u=RePEc:pra:mprapa:129175 |
| By: | Yujiao Chen |
| Abstract: | We study risk-neutral control in Markov decision processes with an absorbing catastrophic state. Even though rewards are linear and the agent has no utility curvature, probability weighting, or framing dependence, standard Bellman optimality produces three prospect-theory-like signatures: an S-shaped value-function profile (convex near catastrophe, concave in the far field), an endogenous loss-sensitivity coefficient $\lambda^*(S) > 1$, and a reflection-effect policy reversal. Across 495 configurations, the optimal policy plays safe near catastrophe in positive-drift (growth) regimes despite the risky action's higher immediate expected value, and plays risky near catastrophe in negative-drift (decline) regimes despite the safe action's lower immediate expected loss. We derive a closed-form expression for the asymptotic loss-aversion plateau $\bar{\lambda}$ that depends only on win probability $p$, payoff asymmetry $r = |\Delta_\ell/\Delta_w|$, and discount factor $\beta$, and matches numerical solutions to $R^2 = 0.999$. The mechanism does not require asymmetric payoffs. Across a sweep of $(p, \beta)$ at three asymmetry levels, the asymmetry share of $\bar{\lambda}$ above unity has median 4.6% at $r = 1.25$ and rises to 13.9% at $r = 2$, with the boundary contribution exceeding the asymmetry contribution in every cell tested. The phenomena persist under tabular Q-learning (a model-free agent reproduces $V^*$ at correlation 0.98 in growth and 1.00 in decline) and under stochastic transitions with Gaussian, heavy-tailed Student-$t_3$, and asymmetric skew-normal noise up to 50% of the step size, where the asymptotic plateau tracks the closed-form prediction within 0.41% for safe-channel noise and within 9.6% for risky-channel or both-channel noise. These results identify absorbing failure states as a sufficient structural mechanism for prospect-theory-like behavior under optimal control. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2606.00970 |
| By: | Yifan Hong; Hongmiao Fan; Chen Wang |
| Abstract: | Decision-making under risk is typically studied through single-shot lottery choices. Yet many real decisions involve combinatorial risk, where risk arises from multiple risky components, so the lottery over outcomes is induced rather than given outright and can be costly to evaluate exactly. We introduce an investment-allocation task to study decision under combinatorial risk, where investing in a component raises its success probability and thereby reshapes the outcome distribution. Participants favor the option with the larger probability increment, and, when increments are equal, the option with the higher initial success probability. Revealing the induced probability mass function (PMF) substantially changes behavior, making participants less responsive to combinatorial-risk features and reducing choice variance. To explain these patterns, we move beyond standard benchmarks and hand-crafted hypotheses with symbolic regression to discover compact descriptive models. The discovered models rely mainly on combinatorial-risk features, such as the after-investment success probability, rather than exact evaluation of the full induced distribution. Behavior under the displayed PMF is then well explained by augmenting this model with a prospect-theoretic residual model. The results show that people navigate combinatorial risk primarily through its core features, shifting toward lottery valuation only when the induced PMF is displayed. |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2606.10092 |
| By: | Andrea Loi; Stefano Matta |
| Abstract: | We study global uniqueness of competitive equilibrium in two-good pure-exchange economies with heterogeneous impatience types and a common HARA Bernoulli utility. The paper connects the CRRA sorting result of \citet{GeanakoplosWalsh2018} with the line of HARA uniqueness results developed in \citet{LoiMatta2022, LoiMatta2024}. In the CRRA case, ordered endowments provide a sorting mechanism for uniqueness. In the HARA case, uniqueness is known to hold for arbitrary endowments under the curvature bound $\gamma\le I/(I-1)$, where $I$ is the number of impatience types. For two types, the curvature restriction can be removed under a monotone sorting condition linking patience and endowment composition. The present paper shows that this high-curvature HARA sorting mechanism is not specific to the two-type case. Our main result proves global uniqueness for any finite number of impatience types and any $\gamma>1$. If types can be ordered so that more patient agents hold weakly more of the first good and weakly less of the second, then the equilibrium price is globally unique. Thus the paper extends the two-type high-curvature HARA result to a genuinely multi-type setting and complements the arbitrary-endowment low-curvature result by replacing the low-curvature restriction with an economically interpretable sorting restriction. In the CRRA subcase ($b=0$), the ordered-endowment condition coincides with that of \citet{GeanakoplosWalsh2018}, and our corollary recovers their uniqueness result. The contribution of the present paper is therefore not the sorting condition itself but its reach: the same ordered heterogeneity in patience and endowment composition rules out multiplicity throughout the shifted HARA case ($b>0$), for any finite number of types and any $\gamma>1$, through a global coefficient-ratio argument. |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2606.11377 |
| By: | Christopher Blier-Wong; Jean-Gabriel Lauzier |
| Abstract: | While risk pooling lowers the total cost of risk, efficiency alone does not make a pool viable. Participants need terms that ensure their participation, that are immune to subgroups breaking away, and that allow new members to join. Under cash-additive risk measures, the minimum cost of a coalition's risk determines the value created by that coalition, and deterministic side payments redistribute that value among participants. Institutional risk sharing is thus a transferable-utility cooperative game. We prove that the game is totally balanced whenever the risk measures are convex (agents are risk averse), so every coalition has a nonempty core and stable allocations always exist. We then analyze entry monotonicity through Population-Monotonic Allocation Schemes (Sprumont, 1990), a strong requirement that is notoriously difficult to construct and has received limited attention in risk sharing. We find several structural conditions that ensure that either the Arrow--Debreu pricing surplus allocation rule or the proportional-cost surplus allocation rule satisfies this entry-monotonicity property, the latter being a novel cooperative notion we propose. These verifiable structural conditions naturally arise in pooled (re)insurance and credit portfolios, providing pool designers with a practical toolkit for building risk pools that remain stable and attractive as they expand. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2606.00972 |
| By: | Ilia Zaznov; Atta Badii; Julian Kunkel; Alfonso Dufour |
| Abstract: | This study addresses the optimal execution of large stock sell programs by introducing TT-DAC-PS (Twin-Target Deterministic Actor-Critic with Policy Smoothing), a deterministic actor-critic architecture that combines twin exponential-moving-average critic targets with pessimistic min backup, TD3-style target policy smoothing noise, delayed actor updates, and conservative Q regularisation to curb overestimation. Exploration uses Ornstein-Uhlenbeck (OU) noise with a hybrid schedule: deterministic episode-wise decay, variance-guided adjustment based on recent reward dispersion, and a Soft Actor-Critic (SAC)-style temperature that is learned and mapped to the noise scale. The environment integrates Almgren-Chriss (AC) trade impact with Limit Order Book (LOB) prices and volumes, normalised state features, per-step volume participation caps, and a utility-based reward. The trade execution algorithm is applied to LOB data for ten U.S. stocks. Performance is assessed against reinforcement-learning baseline algorithms, including Proximal Policy Optimisation (PPO), Soft Actor-Critic (SAC), and Advantage Actor-Critic (A2C), as well as alternative trade execution algorithms, including Time-Weighted Average Price (TWAP), Volume-Weighted Average Price (VWAP), and AC. The proposed model consistently reduces mean implementation shortfall percentage with competitive variance, outperforming classical baselines and standard reinforcement-learning benchmark models. |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2606.08379 |