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on Utility Models and Prospect Theory |
| By: | Rui Dai; Zongxia Liang; Yang Liu |
| Abstract: | The utility function plays a core role in portfolio selection, but its specific form is typically hard to elicit. We propose a definition of the elicited utility function and develop a preference-fitting method to obtain it. Basically, we use intuitive probability-wealth pairs to derive a fitted terminal wealth, a fitted portfolio and a fitted utility function, which converge to the optimal terminal wealth, the optimal portfolio and the elicited utility function of the investor, respectively. Specifically, we first establish a bijection between the utility functions and the terminal wealth functions, based on which we construct the fitted terminal wealth, and then obtain the fitted portfolio and the fitted utility function through the martingale-duality method. Next, we develop a piecewise hyperbolic absolute risk aversion (abbr. PHARA) utility approximation method, and verify the convergences in various senses: almost surely, $L^r$, uniform, etc. We demonstrate two applications of our method: obtaining asymptotically explicit portfolios and handling portfolio selection under Value-at-Risk (abbr. VaR) constraints, thereby illustrating its advantages including intuitiveness, analytical tractability, and ability to circumvent the Lagrange multiplier. |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2607.04346 |
| By: | Fernando Payró Chew; Norio Takeoka; Jianming Xia |
| Abstract: | This paper provides axiomatic foundations for a model in which ambiguity attitudes are endogenously determined through cognitive optimization. The decision maker evaluates acts using alternative non-additive aggregation rules and optimally trades off the benefits of less ambiguity-averse evaluation against cognitive cost. The resulting framework generalizes Choquet expected utility and accounts for preference reversals identified by Machina (2009). The model is characterized by a novel axiom, Comonotonic Convexity, which regulates the evaluation of mixtures by requiring the decision maker to avoid hedging whenever it yields no benefit. We interpret this axiom as reflecting aversion to unnecessary complexity in the evaluation of acts. |
| Keywords: | ambiguity attitude, Choquet expected utility, cognitive optimization, comonotonicity, Machina’s paradox |
| JEL: | D11 D81 |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:bge:wpaper:1587 |
| By: | Wei Ma |
| Abstract: | We present a revealed preference characterization of the discounted expected utility model with a concave utility function. The characterization offers a nonparametric test of the model. We apply the test to an experimental data set in the literature and find that the model is almost always rejected even when all payments involved are subject to risk. |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2606.29779 |
| By: | Bauch, Gerrit (Center for Mathematical Economics, Bielefeld University) |
| Abstract: | I provide an axiomatization of expected utility in which topological continuity is replaced by a geometric axiom. The axiom requires a finite set of indifferent lotteries that span a hyperplane. In the case of three prizes, two indifferent lotteries suffice. The axiom is weaker than Solvability, as well as logically independent of Weak Continuity and the Archimedean axiom. |
| Keywords: | Expected utility representation, finite continuity axiom |
| Date: | 2026–07–27 |
| URL: | https://d.repec.org/n?u=RePEc:bie:wpaper:768 |
| By: | Tirgari, Mohammad; Nejadhashemi, A. Pouyan; Harmel, R. Daren |
| Abstract: | The agricultural economics literature has overlooked the development of a normative approach to describe farmers’ non-monotonic behavior and preferences toward environmental strategies. This gap has become increasingly important as emerging global paradigms related to nitrogen planetary boundaries and the Sustainable Development Goals (SDGs) call for nitrogen regulatory policies that promote pro-environmental behavior. Consequently, any disruption to farmers’ utility may significantly hinder the implementation of strategies based on Less Environmentally Impactful Diets (LEID-based strategies). This study introduces a novel utility function and extends the normative approach for describing farmers’ preferences regarding the trade-off between economic gains and environmental benefits. The performance of the proposed approach is evaluated using metadata from 421 studies conducted on corn farms in the United States and Canada. The utility function and the marginal rate of substitution between corn yield and the LEID index identify four assumptions underlying farmers’ behavioral rules: (i) the marginal utility of crop yield increases as yield rises but declines through its interaction with nitrogen leaching; (ii) the marginal utility of nitrogen leaching increases as leaching intensifies, although this effect is moderated by its interaction with crop yield; (iii) the marginal utilities of crop yield and nitrogen leaching exhibit a negative interaction, where the inverse relationship indicates substitutability between economic gains and environmental benefits; and (iv) nitrogen leaching exhibits diminishing marginal utility as it approaches the drainage-discharge threshold. The results show that the estimated marginal utility of leid, an index representing the production of less environmentally impactful diets, has an inverse relationship with the elasticity between yield and nitrogen leaching. This finding supports the positive effect of pro-environmental behavior on farmers’ utility among those who successfully reduce nitrogen leaching through LEID-based strategies. The structural properties of the proposed utility function therefore provide theoretical support for analyzing farmers’ behavioral responses to LEID-based strategies. |
| Keywords: | Environmental Economics and Policy |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:ags:aaea26:404781 |
| By: | Ale\v{s} \v{C}ern\'y; Johannes Ruf; Martin Schweizer |
| Abstract: | Uniformly weighted divergence preferences (UWDP) introduced in Maccheroni et al. (2006) are an important class of risk-averse preferences that contain as a special case the monotone mean--variance utility. UWDP are characterised by the lowest expected value of an act in $L^\infty$ under an adversarially chosen probability measure combined with the divergence of this measure. Our main result provides an alternative, computationally friendlier formula, which establishes in full generality that UWDP are the translation-invariant hull of state-independent expected utility over $L^0$. Some consequences of the new representation are studied. |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2607.03305 |
| By: | Christian Oliver Ewald |
| Abstract: | The Arrow–Pratt approximation is one of the cornerstones of expected utility theory, providing the classical local approximation of certainty equivalents and risk premia in terms of absolute risk aversion. Despite its widespread use, its mathematical scope and relationship to higher-order risk preferences remain only partially understood. This paper develops a new framework for the analysis of certainty equivalents and dynamic risk premia based on Malliavin calculus and Wiener chaos analysis. We first show that the classical Arrow–Pratt approximation is not asymptotically valid for arbitrary sequences of vanishing risks, thereby identifying precise limitations of the traditional theory. Motivated by this observation, we formulate certainty equivalents dynamically by considering the progressive revelation of uncertainty through a Brownian filtration. Combining Itô calculus, the Clark–Ocone representation and the Wiener chaos decomposition, we derive a complete hierarchy of higher-order dynamic risk premia and obtain explicit representations of the corresponding coefficients in terms of Malliavin derivatives. For mixed Wiener chaos expansions, higher-order preference measures, including prudence and temperance, emerge naturally through interactions between chaos components and are characterised using Bell polynomial representations. Explicit results for quadratic Gaussian functionals and the Vasicek interest-rate model illustrate the theory and identify a broad class of regular Wiener functionals for which the classical Arrow–Pratt approximation is recovered as the leading-order term. The results establish a unified framework linking expected utility theory, stochastic analysis and Wiener chaos expansions, opening a new perspective on higher-order certainty equivalents and the dynamic measurement of risk. |
| Keywords: | Arrow–Pratt approximation; certainty equivalents; risk premium; Malliavin calculus; Wiener chaos expansions; Itô calculus; higher-order risk preferences; expected utility |
| JEL: | D81 C02 C65 C11 |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:gla:glaewp:2026_06 |
| By: | John Mori |
| Abstract: | A representative democracy is immune to gerrymandering if it satisfies Chambers' (2008) representative consistency. We examine preference aggregation and show that representative consistency is mutually inconsistent with three other normative desiderata -- efficiency, anonymity, and neutrality. We show this impossibility result both in a setting with ordinal preferences and a setting with expected utility preferences. |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2607.05660 |
| By: | Jeff Helzner |
| Abstract: | Evaluating decisions made under uncertainty is hard when labeled outcomes are scarce, costly, or confounded with luck. We treat subjective expected utility (SEU) maximization as a stated standard and define a graded measure -- SEU sensitivity -- of an agent's conformity to it. The vehicle is a softmax choice model with a sensitivity parameter $\alpha$ on SEU-valued alternatives; the contribution is a sequence of identifiability results for $\alpha$ and for belief and utility parameters $(\beta, \delta)$, validated in Stan via prior predictive checks, parameter recovery, and simulation-based calibration (SBC), with finite-sample caveats intact. In the uncertain-choice-only model $m_0$, $\alpha$ is identifiable given the expected-utility vector $\eta$ and sharply recovered, while $(\beta, \delta)$ are only weakly informed: the posterior barely contracts and concentrates on a $\beta$-$\delta$ trade-off. In the extended model $m_1$, $\delta$ becomes identifiable in principle via a $\beta$-free risky block, but its practical recovery gain at realistic sample sizes is negligible (matched-count CI-width reduction under 1%), and that block yields no detected $\alpha$-precision gain at matched choice count. These are two distinct phenomena: for $\delta$, identifiability does not imply precise estimability at realistic $n$; for $\alpha$, identifiability is silent about what governs finite-$n$ precision. Marginal SBC passes for both models even where the joint posterior is weakly informed -- a demarcation we make precise. A two-by-two application (GPT-4o and Claude 3.5 Sonnet, each on insurance-claims triage and Ellsberg-style urns, with sampling temperature as the lever) runs end-to-end on real LLM choice data, detecting a structured comparative $\alpha$ effect in two of four cells. |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2607.11920 |
| By: | Hochmuth, Brigitte; Merz, Monika; Prettenthaler, Fabian |
| Abstract: | This paper studies how individual risk attitudes shape occupational choice and wealth accumulation. Using self-reported individual risk preferences from the German Socioeconomic Panel (GSOEP), we estimate that an increase in risk tolerance raises the probability of a worker transitioning to self-employment. We also develop a life-cycle model of occupational choice with Epstein-Zin preferences and heterogeneous risk attitudes to study how risk aversion interacts with entrepreneurial ability and wealth in determining entry into self-employment and its aggregate implications. Counterfactual simulations show that increasing business risk reduces entry but improves selection by entrepreneurial skills. In contrast, Germany’s “1-Euro GmbH†reform of 2008 weakened the role of risk tolerance for entry and increased participation by more risk-averse individuals. |
| Keywords: | Recursive utility |
| JEL: | E21 E24 J24 |
| Date: | 2025–05 |
| URL: | https://d.repec.org/n?u=RePEc:cpr:ceprdp:20286 |
| By: | Mastrobuoni, Giovanni; Owens, Emily |
| Abstract: | This study proposes a new framework to investigate whether criminals exhibit strategic behavior in response to the legal and enforcement environment. Utilizing a unique dataset on commercial robberies in Milan from 2008 to 2010, we examine the decisions robbers make regarding weapon choice, number of accomplices, and the type of business targeted. Our analysis explores the relationship between these decisions, the expected return from the robbery, and the probability of arrest, considering the constraints imposed by Italian law, which prescribes differential punishments based on certain criminal choices. We find some evidence that robbers act in accordance with expected utility maximization, particularly when operating in groups. Our findings suggest that at least some robberies are conducted in a way consistent with rational strategic behavior. |
| Keywords: | Police; Crime |
| JEL: | K42 K14 |
| Date: | 2025–05 |
| URL: | https://d.repec.org/n?u=RePEc:cpr:ceprdp:20237 |
| By: | Dong, Caroline Yifan; Fei, Chengcheng; McCarl, Bruce; Zilberman, David |
| Abstract: | U.S. farmers have reallocated land across crops on an extraordinary scale over the past thirty years, and how much of this reflects climate adaptation matters for the welfare cost of warming. A farmer who switches from cotton to soybean may be chasing higher expected returns or fleeing rising downside risk. The two motives carry very different welfare and policy implications but reduced-form acreage-share methods cannot tell them apart. We build a structural land-use framework in which risk-averse farmers choose among crops by maximizing CARA expected utility over believed non-Gaussian per-acre profit distributions. The believed distributions are constructed from a thirty-year rolling weather belief and a Just–Pope yield model. The acreageshare system estimates a behaviorally disciplined distribution of farmer absolute risk aversion from observed land shares, rather than calibrating it from surveys. Federal crop insurance enters explicitly through its indemnity-and-premium structure. The framework lets us decompose climate-driven between-crop reallocation into a productivity channel and a risk channel, evaluate the welfare value of letting farmers re-optimize across crops, and assess subsidized federal crop insurance as a climate-adaptation policy. We apply the model to U.S. county-level land-allocation data 1987–2022 and project a CMIP6 SSP2-4.5 climate forward to mid-century. Two findings emerge. Between-crop reallocation absorbs most of the welfare cost of climate change the model assigns. About one-third of the projected reallocation reflects substitution away from worsening downside risk rather than toward higher expected returns — a channel reduced-form acreage methods cannot identify — and the same one-third risk share appears retrospectively in the actually-observed 1990–2020 reallocation. |
| Keywords: | Production Economics |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:ags:aaea26:404687 |
| By: | Fei Sun; Wenyuan Wang; Kaixin Yan |
| Abstract: | We study optimal portfolio and consumption in a regime-switching multi-name credit market with default contagion. Defaults generate portfolio losses and alter the intensities of surviving securities. Under Cobb--Douglas utility, homogeneity reduces the HJB equation to a recursive ODE system indexed by the default states. Solving it backward from the all-default state, we establish existence and uniqueness of positive classical solutions, characterize the optimal feedback controls, and prove a verification theorem. |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2607.10542 |
| By: | Giebe, Thomas (Department of Economics and Statistics); Gürtler, Oliver (University of Cologne, Germany) |
| Abstract: | We characterize the production technologies that generate contests strategically equivalent to the standard additive Lazear-Rosen tournament. A contest with a general production function is strategically equivalent to the additive benchmark if and only if the marginal rate of technical substitution (MRTS) between effort and skill is multiplicatively separable, a characterization that links strategically equivalent contests to the classical theory of additive utility representations. The equivalence class is large: it contains the multiplicative, Cobb-Douglas, CES, and quasilinear technologies, so that, within the class, additivity is a normalization rather than an economic assumption, and existing results for additive contests, e.g., on optimal prize structures and on the effects of noise on effort, extend to the entire class. Strategic equivalence does not, however, make the technology irrelevant for contest design: the equivalence preserves only ordinal information, whereas optimal prize structures depend on cardinal features of the environment. Strategically equivalent technologies can therefore call for opposite prize structures under the same skill distribution. In particular, when skills are exponentially distributed, the case in which all prize structures perform equally well in the additive model, the monotonicity of the MRTS in skill alone determines whether the winner-takes-all or the loser-gets-nothing contest is optimal. |
| Keywords: | contest; strategic equivalence; production function; MRTS; contest design; prize structure |
| JEL: | C72 D11 D74 D86 |
| Date: | 2026–07–29 |
| URL: | https://d.repec.org/n?u=RePEc:hhs:vxesta:2026_003 |
| By: | Wong, Wing-Keung |
| Abstract: | Employing both mean-variance portfolio optimization and stochastic dominance analysis, we examine whether including Bitcoin and a 3-month US Treasury-Bill could generate arbitrage opportunities and lead to a better investment choice. The results show, independent of whether short sales are allowed, that: (1) investors are generally indifferent to portfolios with Bitcoin and without Bitcoin; (2) investors prefer to invest in portfolios with Treasury-Bill than portfolios without Treasury Bill to gain higher expected utility but not a higher expected wealth; and (3) portfolios with both Bitcoin and a Treasury-Bill dominate the ones without Bitcoin and Treasury-Bill, at the first, second and third order. Asubperiod analysis confirms the above results, indicating that investors can earn abnormal returns when both Bitcoin and Treasury-Bills are included in the portfolio. Through robustness checks using varying portfolio sizes and excluding outliers, we confirm the consistency and reliability of our findings. Our findings can be used by investors in their investment processes, and reveal the arbitrary opportunities when Bitcoin and a 3-month US Treasury-Bill is included in the investment. |
| Keywords: | Bitcoin; Treasury bill; mean-variance portfolio optimization; stochastic dominance; arbitrage opportunities |
| JEL: | G0 |
| Date: | 2025–06–26 |
| URL: | https://d.repec.org/n?u=RePEc:pra:mprapa:130021 |
| By: | Fan, Ying; Fan, Ziying; Zhou, Yiyi |
| Abstract: | This paper studies how dynamic changes in the search environment affect consumer search and purchase behavior. We develop a dynamic model that incorporates a non-stationary search environment and propose a feasible estimation procedure to estimate its parameters. We apply our model and estimation procedure to the Beijing housing market, utilizing detailed data on consumers' complete search records. We show that accounting for dynamics is crucial for accurately estimating search costs. Additionally, we find that search environment dynamics have a significant impact on consumer decisions and welfare. Housing supply policies that alter search environment dynamics---by increasing the number of new listings and slowing down price increases---benefit consumers, primarily by incentivizing longer searches, more property visits, and ultimately leading to purchases that yield higher utility. |
| JEL: | D8 L8 R3 |
| Date: | 2025–02 |
| URL: | https://d.repec.org/n?u=RePEc:cpr:ceprdp:19957 |