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on Utility Models and Prospect Theory |
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Issue of 2024‒07‒29
eleven papers chosen by |
| By: | Len Patrick Dominic M. Garces; Yang Shen |
| Abstract: | We investigate a continuous-time investment-consumption problem with model uncertainty in a general diffusion-based market with random model coefficients. We assume that a power utility investor is ambiguity-averse, with the preference to robustness captured by the homothetic multiplier robust specification, and the investor's investment and consumption strategies are constrained to closed convex sets. To solve this constrained robust control problem, we employ the stochastic Hamilton-Jacobi-Bellman-Isaacs equations, backward stochastic differential equations, and bounded mean oscillation martingale theory. Furthermore, we show the investor incurs (non-negative) utility loss, i.e. the loss in welfare, if model uncertainty is ignored. When the model coefficients are deterministic, we establish formally the relationship between the investor's robustness preference and the robust optimal investment-consumption strategy and the value function, and the impact of investment and consumption constraints on the investor's robust optimal investment-consumption strategy and value function. Extensive numerical experiments highlight the significant impact of ambiguity aversion, consumption and investment constraints, on the investor's robust optimal investment-consumption strategy, utility loss, and value function. Key findings include: 1) short-selling restriction always reduces the investor's utility loss when model uncertainty is ignored; 2) the effect of consumption constraints on utility loss is more delicate and relies on the investor's risk aversion level. |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2407.02831&r= |
| By: | Keyu Wu; Ernst Fehr; Sean Hofland; Martin Schonger |
| Abstract: | Ambiguous prospects are ubiquitous in social and economic life, but the psychological foundations of behavior under ambiguity are still not well understood. One of the most robust empirical regularities is the strong correlation between attitudes towards ambiguity and compound risk which suggests that compound risk aversion may provide a psychological foundation for ambiguity aversion. However, compound risk aversion and ambiguity aversion may also be independent psychological phenomena, but what would then explain their strong correlation? We tackle these questions by training a treatment group’s ability to reduce compound to simple risks, and analyzing how this affects their compound risk and ambiguity attitudes in comparison to a control group who is taught something unrelated to reducing compound risk. We find that aversion to compound risk disappears almost entirely in the treatment group, while the aversion towards both artificial and natural sources of ambiguity remain high and are basically unaffected by the teaching of how to reduce compound lotteries. Moreover, similar to previous studies, we observe a strong correlation between compound risk aversion and ambiguity aversion, but this correlation only exists in the control group while in the treatment group it is rather low and insignificant. These findings suggest that ambiguity attitudes are not a psychological relative, and derived from, attitudes towards compound risk, i.e., compound risk aversion and ambiguity aversion do not share the same psychological foundations. While compound risk aversion is primarily driven by a form of bounded rationality – the inability to reduce compound lotteries – ambiguity aversion is unrelated to this inability, suggesting that ambiguity aversion may be a genuine preference in its own right. |
| Keywords: | ambiguity aversion, compound risk aversion, bounded rationality, reduction of compound lotteries |
| JEL: | C91 D01 D91 |
| Date: | 2024 |
| URL: | https://d.repec.org/n?u=RePEc:ces:ceswps:_11150&r= |
| By: | Wilfried Youmbi |
| Abstract: | The Random Utility Model (RUM) is the gold standard in describing the behavior of a population of consumers. The RUM operates under the assumption of transitivity in consumers' preference relationships, but the empirical literature has regularly documented its violation. In this paper, I introduce the Random Preference Model (RPM), a novel framework for understanding the choice behavior in a population akin to RUMs, which preserves monotonicity and accommodates nontransitive behaviors. The primary objective is to test the null hypothesis that a population of rational consumers generates cross-sectional demand distributions without imposing constraints on the unobserved heterogeneity or the number of goods. I analyze data from the UK Family Expenditure Survey and find evidence that contradicts RUMs and supports RPMs. These findings underscore RPMs' flexibility and capacity to explain a wider spectrum of consumer behaviors compared to RUMs. This paper generalizes the stochastic revealed preference methodology of McFadden & Richter (1990) for finite choice sets to settings with nontransitive and possibly nonconvex preference relations. |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2406.13969&r= |
| By: | Luca Anderlini (Georgetown University, University of Naples Federico II and CSEF); Joshua C. Teitelbaum (Georgetown University) |
| Abstract: | Part of a ship’s cargo is jettisoned in order to save the vessel and the remaining cargo from imminent peril. How should the loss be shared among the cargo owners? The law of general average, an ancient principle of maritime law, prescribes that the owners share the loss proportionally according to the respective values of their cargo. We analyze whether the law of general average is a truthful and efficient mechanism. That is, we investigate whether it induces truthful reporting of cargo values and yields a Pareto efficient allocation in equilibrium. We show that the law of general average is neither truthful nor efficient if owners have expected utility preferences, but is both truthful and efficient if owners have maxmin utility preferences. We discuss why maxmin behavior may be reasonable in the general average context. |
| Keywords: | general average, loss sharing, maritime law, maxmin, mutual insurance, truthful equilibrium, Pareto efficiency. |
| JEL: | C72 D82 G22 K39 |
| Date: | 2024–06–26 |
| URL: | https://d.repec.org/n?u=RePEc:sef:csefwp:725&r= |
| By: | Helmuth Cremer; Jean-Marie Lozachmeur |
| Abstract: | We study the design of nonlinear reimbursement rules for expenses on secondary preventive and on therapeutic care. With some probability individuals are healthy and do not need any therapeutic health care. Otherwise they become ill and the severity of their disease is realized and identifies their ex post type. Preventive care is determined ex ante, that is before the health status is determined while curative care is chosen ex post. Insurance benefits depend on preventive and curative care in a possibly nonlinear way, and marginal benefits can be positive or negative. In the first best, achieved when health status is ex post publicly observable, insurance benefits are flat (lump sum payments) and do not depend on expenditures. When the severity of the disease is not observable, so that there is ex post moral hazard, this solution is not incentive compatible (for more healthy individuals). The optimal insurance then implies benefits that increase with both types of care. This is because health expenditures reduce informational rents and they are upward distorted. This relaxes the incentive constraint because less healthy individuals value care more than healthy individuals. Even though preventive care is chosen ex ante, when there is no asymmetry of information, it does have an impact on the incentive constraint and thus on informational rents. This is due to two concurring effects. First, prevention is more effective for the more severely ill. Second, these individuals also have a lower marginal utility of income so that a given level of expenditure on preventive care has less impact on their utility. |
| Keywords: | ex post moral hazard, health insurance, secondary prevention |
| JEL: | I11 I13 I18 |
| Date: | 2024 |
| URL: | https://d.repec.org/n?u=RePEc:ces:ceswps:_11186&r= |
| By: | Anna Bogomolnaia; Herv\'e Moulin |
| Abstract: | In a general fair division model with transferable utilities we discuss endogenous lower and upper guarantees on individual shares of benefits or costs. Like the more familiar exogenous bounds on individual shares described by an outside option or a stand alone utility, these guarantees depend on my type but not on others' types, only on their number and the range of types. Keeping the range from worst share to best share as narrow as permitted by the physical constraints of the model still leaves a large menu of tight guarantee functions. We describe in detail these design options in several iconic problems where each tight pair of guarantees has a clear normative meaning: the allocation of indivisible goods or costly chores, cost sharing of a public facility and the exploitation of a commons with substitute or complementary inputs. The corresponding benefit or cost functions are all sub- or super-modular, and for this class we characterise the set of minimal upper and maximal lower guarantees in all two agent problems. |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2406.14198&r= |
| By: | Simon K. Schnyder; John J. Molina; Ryoichi Yamamoto; Matthew S. Turner |
| Abstract: | Faced with a dangerous epidemic humans will spontaneously social distance to reduce their risk of infection at a socio-economic cost. Compartmentalised epidemic models have been extended to include this endogenous decision making: Individuals choose their behaviour to optimise a utility function, self-consistently giving rise to population behaviour. Here we study the properties of the resulting Nash equilibria, in which no member of the population can gain an advantage by unilaterally adopting different behaviour. We leverage a new analytic solution to obtain, (1) a simple relationship between rational social distancing behaviour and the current number of infections; (2) new scaling results for how the infection peak and number of total cases depend on the cost of contracting the disease; (3) characteristic infection costs that divide regimes of strong and weak behavioural response and depend only on the basic reproduction number of the disease; (4) a closed form expression for the value of the utility. We discuss how these analytic results provide a deep and intuitive understanding into the disease dynamics, useful for both individuals and policymakers. In particular the relationship between social distancing and infections represents a heuristic that could be communicated to the population to encourage, or "bootstrap", rational behaviour. |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2407.04366&r= |
| By: | Pierre Bardier; Bach Dong-Xuan; Van-Quy Nguyen |
| Abstract: | We propose a new model of incomplete preferences under uncertainty, which we call unanimous dual-self preferences. Act f is considered more desirable than act g when, and only when, both the evaluation of an optimistic self, computed as the welfare level attained in a best-case scenario, and that of a pessimistic self, computed as the welfare level attained in a worst-case scenario, rank f above g. Our comparison criterion involves multiple priors, as best and worst cases are determined among sets of probability distributions, and is, generically, less conservative than Bewley preferences and twofold multi-prior preferences, the two ambiguity models that are closest to ours |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2406.11166&r= |
| By: | Ahmed, Muhammad Ashfaq; Nawaz, Nasreen |
| Abstract: | Objective: Previous literature on optimal savings relies on specific utility and production technology functional forms which might not be able to produce robust results as different utility/production functions may lead to dramatically different or opposing results. This paper derives an optimal savings policy based on parameters (such as slopes of demand and supply curves) which can be empirically estimated and provides a unique and robust result irrespective of shape and form of individual utilities/production functions. Furthermore, existing literature does not consider welfare loss when savings market is adjusting to final equilibrium after a shock while deriving an optimal savings policy. In addition to that, number of savers (all public and private saving entities, including households, firms, etc., ) and saving rate are vital parameters for savings in an economy, and while deriving an optimal savings policy, it is necessary to take into consideration these parameters to ensure that quantum of savings due to interest rate movement gets adjusted in target time duration, without which there may be additional efficiency loss than that envisioned while deriving an optimal savings policy for an economy. Methods: This research project designs a dynamical model for savings market and extends that to a three-dimensional savings system in an economy by taking into consideration number of savers, saving rate, and interest rate; and based on that derives an optimal comprehensive savings policy while accounting for efficiency losses when savings market, saving rate, and number of savers are adjusting to final equilibrium, in addition to the welfare loss on account of equilibrium shift. Results: Without consideration of welfare loss/gain while savings market is adjusting after implementation of a savings policy, welfare picture remains incomplete, and the optimal savings policy based on partial welfare cannot be considered as optimal in true sense. Traditionally, welfare of only producer and consumer is taken into consideration without accounting for welfare of production factors. An expression of efficiency loss/gain as a result of savings policy based on welfare including those of production factors has been presented and optimal savings policies have been derived by minimizing efficiency losses and presented as a final result in the form of mathematical expressions. This paper demonstrates that both supply and demand shocks operate through a common channel, i.e., inventory of funds in savings market as both kinds of shock affect inventory of funds and hence can be categorized just as an inventory shock. Conclusion: For optimal welfare gains, practitioners/policy makers must estimate theoretically derived optimal savings policies based on the dynamic model developed in this paper and presented in the form of mathematical expressions from real world relevant data for implementation. |
| Keywords: | Savings, Saving Rate, Optimal Policy, Dynamic Path, Equilibrium, Coordination |
| JEL: | E21 G10 G18 |
| Date: | 2023–08–11 |
| URL: | https://d.repec.org/n?u=RePEc:pra:mprapa:121352&r= |
| By: | Arno Apffelstaedt (University of Cologne); Gönül Doğan (University of Cologne); Fabian Hoffmann (University of Cologne) |
| Abstract: | We introduce a novel concept, group image concerns, showing that individuals change their behavior and are willing to incur personal costs to cultivate a positive image of their groups. We develop an experimental method to identify and quantify group image concerns, and conduct a series of laboratory and online experiments to measure them in three distinct domains. In the first two experiments focused on charitable behavior, participants donate more when their contributions are publicly associated with their group, despite their individual identity remaining private. They also pay significant amounts to keep low donations from other group members private and to make high donations public. These findings emerge for students in the laboratory, using university affiliation as their group identity, as well as for online participants from the general U.S. population, using religious affiliation as their group identity. Additional online experiments explore group image concerns among Democrats and Republicans regarding their group’s knowledge of the U.S. national anthem, as a measure of patriotism, and among U.S. students concerning their university’s reputation for intelligence in solving matrix completion tasks. We isolate group image concerns from individual image concerns and benchmark them against individual image concerns in our laboratory experiment. Our results establish group image concerns as an important driver of individual behavior and a significant source of utility across various domains. |
| Keywords: | social identity and behavior, image concerns, experiments, charitable and prosocial behavior, intelligence, political identity, religious identity, real effort |
| JEL: | D01 D91 C92 |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:ajk:ajkdps:324&r= |
| By: | Robinson, Thomas; Tax, Niek; Mudd, Richard; Guy, Ido |
| Abstract: | Active learning can improve the efficiency of training prediction models by identifying the most informative new labels to acquire. However, non-response to label requests can impact active learning’s effectiveness in real-world contexts. We conceptualise this degradation by considering the type of non-response present in the data, demonstrating that biased non-response is particularly detrimental to model performance. We argue that biased non-response is likely in contexts where the labelling process, by nature, relies on user interactions. To mitigate the impact of biased non-response, we propose a cost-based correction to the sampling strategy–the Upper Confidence Bound of the Expected Utility (UCB-EU)–that can, plausibly, be applied to any active learning algorithm. Through experiments, we demonstrate that our method successfully reduces the harm from labelling non-response in many settings. However, we also characterise settings where the non-response bias in the annotations remains detrimental under UCB-EU for specific sampling methods and data generating processes. Finally, we evaluate our method on a real-world dataset from an e-commerce platform. We show that UCB-EU yields substantial performance improvements to conversion models that are trained on clicked impressions. Most generally, this research serves to both better conceptualise the interplay between types of non-response and model improvements via active learning, and to provide a practical, easy-to-implement correction that mitigates model degradation. |
| Keywords: | active learning; non-response; missing data; e-commerce; CTR prediction; Springer deal |
| JEL: | L81 |
| Date: | 2024–05–25 |
| URL: | https://d.repec.org/n?u=RePEc:ehl:lserod:123029&r= |