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on Utility Models and Prospect Theory |
| By: | Preker, Jurek (Center for Mathematical Economics, Bielefeld University) |
| Abstract: | We investigate and axiomatize preferences that display indifference between deterministic states, but exhibit strict orderings over lotteries over these states. Such preferences might be due to the ability to adopt to states, or a (dis)taste for uncertainty. We derive a representation theorem for preferences that are symmetric—that is, a decision maker is indifferent between a lottery and its permutations over the set of states—, continuous, and satisfy a weakened version of independence. We then describe when these preferences exhibit a taste or distaste for uncertainty. Finally, we characterize pairs of lotteries for which every uncertainty-averse decision maker prefers one of the lotteries over the other one. |
| Keywords: | Expected Utility, Induced Preferences, Mixture Aversion |
| Date: | 2026–01–28 |
| URL: | https://d.repec.org/n?u=RePEc:bie:wpaper:761 |
| By: | Collin Raymond; Yangwei Song |
| Abstract: | We extend well-known comparative results under expected utility to models of non-expected utility by providing novel conditions on local utility functions. We illustrate how our results parallel, and are distinct from, existing results for monotone comparative statics under expected utility, as well as risk preferences for non-expected utility. Our conditions generalize existing results for specific preferences (including expected utility) and allow us to verify monotone comparative statics for novel environments and preferences. We apply our results to portfolio choice problems where preferences or wealth might change, as well as precautionary savings. |
| Date: | 2026–01 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2601.10664 |
| By: | Leo Kurata; Kensei Nakamura |
| Abstract: | This paper studies preference aggregation under risk. In our model, each agent has an incomplete preference relation represented by a set of expected utility functions. The classical Pareto principle is silent on agreement involving indecisiveness. To examine the implications of respecting such agreement, we introduce the Paretian principle that can be applied when some individuals reserve their judgment. Our main result shows that, under this principle, for each combination of individuals' utility functions, there exists a corresponding social utility function constructed as a weighted sum of the individual ones. These aggregation rules guarantee natural properties that the standard Pareto principle fails to ensure. |
| Date: | 2026–01 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2601.01334 |
| By: | Laurence Carassus; Mikl\'os R\'asonyi |
| Abstract: | We consider an investor who, while maximizing his/her expected utility, also compares the outcome to a reference entity. We recall the notion of personal equilibrium and show that, in a multistep, generically incomplete financial market model such an equilibrium indeed exists, under appropriate technical assumptions. |
| Date: | 2025–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2512.08348 |
| By: | Xia Han; Bin Li; Yao Luo |
| Abstract: | We propose a new framework for studying optimal insurance under information asymmetry within the Stackelberg game framework. In this setting, a monopolistic insurer faces uncertainty regarding a customer's loss distribution or risk attitude. The customer is assumed to follow a mean–variance preference in continuous time, while the insurer sets premiums through a risk loading based on the expected loss. An optimal menu is explicitly derived for a general class of aggregate loss models. Our approach connects with the extensive literature on optimal insurance demand, stemming from the seminal work of Arrow (1963), and leads to an interesting finding: a nonlinear pricing structure for risk-type uncertainty versus a linear pricing structure for risk-attitude uncertainty. Specifically, if an insurer is uncertain about a customer's risk type and seeks to elicit this information, the risk loading (premium minus expected loss) is set lower for high-risk individuals to encourage them to select the corresponding contract. In contrast, if the insurer is only uncertain about the customer's risk attitude, no such discounts---in terms of risk loading---are provided. This reveals that information about customers' risk types is more valuable than information about their risk attitudes. Additionally, we compare our optimal menu with the worst-case contract derived from the maxmin expected utility, we find that our optimal menu increases the insurer's expected profit and enhances the likelihood of trading. |
| Keywords: | Optimal insurance; Information asymmetry; Stackelberg game framework; Risk loading; Nonlinear pricing; Linear pricing; Ambiguity |
| JEL: | D82 G22 D81 |
| Date: | 2026–01–22 |
| URL: | https://d.repec.org/n?u=RePEc:tor:tecipa:tecipa-815 |
| By: | Xiangxin He; Fangda Liu; Ruodu Wang |
| Abstract: | Portfolio diversification is a cornerstone of modern finance, while risk aversion is central to decision theory; both concepts are long-standing and foundational. We investigate their connections by studying how different forms of diversification correspond to notions of risk aversion. We focus on the classical distinctions between weak and strong risk aversion, and consider diversification preferences for pairs of risks that are identically distributed, comonotonic, antimonotonic, independent, or exchangeable, as well as their intersections. Under a weak continuity condition and without assuming completeness of preferences, diversification for antimonotonic and identically distributed pairs implies weak risk aversion, and diversification for exchangeable pairs is equivalent to strong risk aversion. The implication from diversification for independent pairs to weak risk aversion requires a stronger continuity. We further provide results and examples that clarify the relationships between various diversification preferences and risk attitudes, in particular justifying the one-directional nature of many implications. |
| Date: | 2026–01 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2601.04067 |
| By: | Peter J. Hammond |
| Abstract: | In normative models a decision-maker is usually assumed to be Bayesian rational, and so to maximize subjective expected utility, within a complete and correctly specified decision model. Following the discussion in Hammond (2007) of Schumpeter's (1911, 1934) concept of entrepreneurship, as well as Shackle's (1953) concept of potential surprise, we consider enlivened decision trees whose growth over time cannot be accurately modelled in full detail. An enlivened decision tree involves more severe limitations than a mis-specified model, unforeseen contingencies, or unawareness, all of which are typically modelled with reference to a universal state space large enough to encompass any decision model that an agent may consider. We consider a motivating example based on Homer's classic tale of Odysseus and the Sirens. Though our novel framework transcends standard notions of risk or uncertainty, for finite decision trees that may be truncated because of bounded rationality, an extended and refined form of Bayesian rationality is still possible, with real-valued subjective evaluations instead of consequences attached to terminal nodes where truncations occur. Moreover, these subjective evaluations underlie, for example, the kind of Monte Carlo tree search algorithm used by recent chess-playing software packages. They may also help rationalize the contentious precautionary principle. |
| Date: | 2026–01 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2601.06405 |
| By: | Gregorio Curello; Ludvig Sinander; Mark Whitmeyer |
| Abstract: | In choice under risk, there is a standard notion of 'less risk-averse than', due to Yaari (1969). In the theory of comparative statics, the single-crossing property is satisfied by all weighted averages of a family of single-crossing functions if and only if the family satisfies a property called signed-ratio monotonicity (Quah & Strulovici, 2012). We establish a close link between 'less risk-averse than' and signed-ratio monotonicity. |
| Date: | 2025–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2512.06005 |
| By: | Craig S Wright |
| Abstract: | Forecasting accuracy is routinely optimised in financial prediction tasks even though investment and risk-management decisions are executed under transaction costs, market impact, capacity limits, and binding risk constraints. This paper treats forecasting as an econometric input to a constrained decision problem. A predictive distribution induces a decision rule through a utility objective combined with an explicit friction operator consisting of both a cost functional and a feasible-set constraint system. The econometric target becomes minimisation of expected decision loss net of costs rather than minimisation of prediction error. The paper develops a utility-weighted calibration criterion aligned to the decision loss and establishes sufficient conditions under which calibrated predictive distributions weakly dominate uncalibrated alternatives. An empirical study using a pre-committed nested walk-forward protocol on liquid equity index futures confirms the theory: the proposed utility-weighted calibration reduces realised decision loss by over 30\% relative to an uncalibrated baseline ($t$-stat -30.31) for loss differential and improves the Sharpe ratio from -3.62 to -2.29 during a drawdown regime. The mechanism is identified as a structural reduction in the frequency of binding constraints (from 16.0\% to 5.1\%), preventing the "corner solution" failures that characterize overconfident forecasts in high-friction environments. |
| Date: | 2026–01 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2601.07852 |