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on Utility Models and Prospect Theory |
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Issue of 2023‒08‒21
seventeen papers chosen by |
| By: | Gianluca Cassese |
| Abstract: | We obtain an elementary characterization of expected utility based on a representation of choice in terms of psychological gambles, which requires no assumption other than coherence between ex-ante and ex-post preferences. Weaker version of coherence are associated with various attitudes towards complexity and lead to a characterization of minimax or Choquet expected utility. |
| Keywords: | Arbitrage, Choquet expected utility, Coherence, Conglomerability, Expected utility, Gamble, Maxmin expected utility, Multiple priors |
| JEL: | D81 G12 |
| Date: | 2023–07 |
| URL: | http://d.repec.org/n?u=RePEc:mib:wpaper:524&r=upt |
| By: | Shuaijie Qian; Chen Yang |
| Abstract: | This paper studies a finite-horizon portfolio selection problem with non-concave terminal utility and proportional transaction costs. The commonly used concavification principle for terminal value is no longer valid here, and we establish a proper theoretical characterization of this problem. We first give the asymptotic terminal behavior of the value function, which implies any transaction close to maturity only provides a marginal contribution to the utility. After that, the theoretical foundation is established in terms of a novel definition of the viscosity solution incorporating our asymptotic terminal condition. Via numerical analyses, we find that the introduction of transaction costs into non-concave utility maximization problems can prevent the portfolio from unbounded leverage and make a large short position in stock optimal despite a positive risk premium and symmetric transaction costs. |
| Date: | 2023–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2307.02178&r=upt |
| By: | Yoram Halevy; David Walker-Jones; Lanny Zrill |
| Abstract: | We investigate the problem of identifying incomplete preferences in the domain of uncertainty by proposing an incentive-compatible mechanism that bounds the behavior that can be rationalized by very general classes of complete preferences. Hence, choices that do not abide by the bounds indicate that the decision maker cannot rank the alternatives. Data collected from an experiment that implements the proposed mechanism indicates that when choices cannot be rationalized by Subjective Expected Utility they are usually incompatible with general models of complete preferences. Moreover, behavior that is indicative of incomplete preferences is empirically associated with deliberate randomization. |
| Keywords: | Incomplete Preferences, Identification, Elicitation, Choice Under Uncertainty, Deliberate Randomization, Experiment |
| JEL: | C91 D01 D81 D9 |
| Date: | 2023–07–25 |
| URL: | http://d.repec.org/n?u=RePEc:tor:tecipa:tecipa-753&r=upt |
| By: | Ehsan Azmoodeh; Ozan H\"ur |
| Abstract: | In the landmark article \cite{Muller}, M\"uller et. al. introduced the notion of fractional stochastic dominance (SD) to interpolate between first and second SD relations. In this article, we introduce a novel family of \textit{multi-fractional} stochastic orders that generalizes fractional SD in a natural manner. The family of multi-fractional SD is parametrized by an arbitrary non-decreasing function $\gamma$ ranging between $0$ and $1$ which provides the feature of local interpolation rather than a global one. We show that the multi-fractional $(1+\gamma)$-SD is generated by a class of increasing utility functions allowing local non-concavity where the steepness of the non-concavity depends on its location and it is controlled by function $\gamma$. We also introduced the notion of \text{local greediness} that allows us, among other things, to systematically study multi-fractional utility class. The multi-fractional utility class is well-suited for representing a decision maker's preferences in terms of risk aversion and greediness at a local level. Several basic properties as well as illustrating examples are presented. |
| Date: | 2023–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2307.08651&r=upt |
| By: | Quante, Lennart; Otto, Christian; Willner, Sven Norman (Potsdam Institute for Climate Impact Research (PIK)); Middelanis, Robin; Levermann, Anders |
| Abstract: | The behavior of consumers is one of the elementary market forces. Thus, changes in consumed quantity in response to changing prices are an important determinant of economic behavior. Here, we show analytically under minimal assumptions that in an out-of-equilibrium market it can be rational to buy more of a good in spite of increasing prices. When rational consumers maximize their utility, consumption is driven by two factors, the relative price change of goods and their substitutability. Influenced by heterogeneous prices between suppliers and goods, the budget-driven preference for goods with the least price increase is competing with the utility-driven substitution of goods. This leads to a stabilizing feedback loop emerging from any utility function that is strictly monotonically increasing. We illustrate this feedback dynamics in an agent-based model with utility-optimizing consumers under regionally heterogeneous weather-induced supply failures. The resulting relation between changes in prices and quantities are predominantly in line with macro economic observations, but a positive correlation between price and quantity emerges in out-of-equilibrium situations. Thus, in a stressed economy rational consumers might buy more of pricier goods in spite of budget constraints. |
| Date: | 2023–07–10 |
| URL: | http://d.repec.org/n?u=RePEc:osf:osfxxx:n2tqh&r=upt |
| By: | Giulio Principi; Peter P. Wakker; Ruodu Wang |
| Abstract: | Comonotonicity ("same variation") of random variables minimizes hedging possibilities and has been widely used in many fields. Comonotonic restrictions of traditional axioms have led to impactful inventions in decision models, including Gilboa and Schmeidler's ambiguity models. This paper investigates antimonotonicity ("opposite variation"), the natural counterpart to comonotonicity, minimizing leveraging possibilities. Surprisingly, antimonotonic restrictions of traditional axioms often do not give new models but, instead, give generalized axiomatizations of existing ones. We, thus, generalize: (a) classical axiomatizations of linear functionals through Cauchy's equation; (b) as-if-risk-neutral pricing through no-arbitrage; (c) subjective probabilities through bookmaking; (d) Anscombe-Aumann expected utility; (e) risk aversion in Savage's subjective expected utility. In each case, our generalizations show where the most critical tests of classical axioms lie: in the antimonotonic cases (maximal hedges). We, finally, present cases where antimonotonic restrictions do weaken axioms and lead to new models, primarily for ambiguity aversion in nonexpected utility. |
| Date: | 2023–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2307.08542&r=upt |
| By: | Levon Barseghyan; Francesca Molinari |
| Abstract: | We provide sufficient conditions for semi-nonparametric point identification of a mixture model of decision making under risk, when agents make choices in multiple lines of insurance coverage (contexts) by purchasing a bundle. As a first departure from the related literature, the model allows for two preference types. In the first one, agents behave according to standard expected utility theory with CARA Bernoulli utility function, with an agent-specific coefficient of absolute risk aversion whose distribution is left completely unspecified. In the other, agents behave according to the dual theory of choice under risk(Yaari, 1987) combined with a one-parameter family distortion function, where the parameter is agent-specific and is drawn from a distribution that is left completely unspecified. Within each preference type, the model allows for unobserved heterogeneity in consideration sets, where the latter form at the bundle level -- a second departure from the related literature. Our point identification result rests on observing sufficient variation in covariates across contexts, without requiring any independent variation across alternatives within a single context. We estimate the model on data on households' deductible choices in two lines of property insurance, and use the results to assess the welfare implications of a hypothetical market intervention where the two lines of insurance are combined into a single one. We study the role of limited consideration in mediating the welfare effects of such intervention. |
| Date: | 2023–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2307.09411&r=upt |
| By: | Yuki Oyama |
| Abstract: | This study performs an attribute-level analysis of the global and local path preferences of network travelers. To this end, a reward decomposition approach is proposed and integrated into a link-based recursive (Markovian) path choice model. The approach decomposes the instantaneous reward function associated with each state-action pair into the global utility, a function of attributes globally perceived from anywhere in the network, and the local utility, a function of attributes that are only locally perceived from the current state. Only the global utility then enters the value function of each state, representing the future expected utility toward the destination. This global-local path choice model with decomposed reward functions allows us to analyze to what extent and which attributes affect the global and local path choices of agents. Moreover, unlike most adaptive path choice models, the proposed model can be estimated based on revealed path observations (without the information of plans) and as efficiently as deterministic recursive path choice models. The model was applied to the real pedestrian path choice observations in an urban street network where the green view index was extracted as a visual street quality from Google Street View images. The result revealed that pedestrians locally perceive and react to the visual street quality, rather than they have the pre-trip global perception on it. Furthermore, the simulation results using the estimated models suggested the importance of location selection of interventions when policy-related attributes are only locally perceived by travelers. |
| Date: | 2023–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2307.08646&r=upt |
| By: | Nie, Georege Yulin (Concordia University) |
| Abstract: | Markowitz (1952) asset risk has long been challenged. First, asset risk has to be cumulative, because asset holder’s risk approaches zero as time length approaches zero (Nie, 2022a). Second, volatility does not decrease asset value while volatility of a lognormal distribution actually raises asset value. Third, support to Markowitz asset risk appears to arise from a confusion between asset value and wealth utility—the law of diminishing marginal utility supports that volatility reduces the latter. To address the challenges, we argue that asset risk causes volatility, but not vice versa, implying that volatility improperly represents asset risk, which cannot be diversified away. We delineate expected value (which asset risk impacts without a distribution) and volatility (which does not affect the former while following a quasi-normal distribution we proposed). We show that our firm risk, captured as equity risk premium, solves issues that have long been challenging agency and contracting theories. |
| Date: | 2023–07–13 |
| URL: | http://d.repec.org/n?u=RePEc:osf:socarx:tgvb2&r=upt |
| By: | Jarrod Burgh; Emerson Melo |
| Abstract: | We develop a model of wishful thinking that incorporates the costs and benefits of biased beliefs. We establish the connection between distorted beliefs and risk, revealing how wishful thinking can be understood in terms of risk measures. Our model accommodates extreme beliefs, allowing wishful-thinking decision-makers to assign zero probability to undesirable states and positive probability to otherwise impossible states. Furthermore, we establish that wishful thinking behavior is equivalent to quantile-utility maximization for the class of threshold beliefs distortion cost functions. Finally, exploiting this equivalence, we derive conditions under which an optimistic decision-maker prefers skewed and riskier choices. |
| Date: | 2023–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2307.02422&r=upt |
| By: | Pierpaolo Battigalli; Davide Bordoli |
| Abstract: | We analyze the infinite repetition with imperfect feedback of a simultaneous or sequential game, assuming that players are strategically sophisticated---but possibly impatient---expected-utility maximizers. Sophisticated strategic reasoning in the repeated game is combined with belief updating to provide a foundation for a refinement of self-confirming equilibrium. In particular, we model strategic sophistication as rationality and common strong belief in rationality. Then, we combine belief updating and sophisticated reasoning to provide sufficient conditions for a kind of learning--that is, the ability, in the limit, to exactly forecast the sequence of future observations--thus showing that impatient agents end up playing a sequence of self-confirming equilibria in strongly rationalizable conjectures of the one-period game. We also provide a converse of this result. Irrespective of whether individuals value the future, if they are able to learn then they will play in the limit a self-confirming equilibrium in strongly rationalizable conjectures of the continuation (infinitely repeated) game. Keywords: Self-confirming equilibrium; Common strong belief in rationality; Learning; Repeated games JEL classification: C72 ; C73 ; D83 |
| Date: | 2023 |
| URL: | http://d.repec.org/n?u=RePEc:igi:igierp:702&r=upt |
| By: | Roland Bénabou; Armin Falk; Luca Henkel; Jean Tirole |
| Abstract: | We analyze how the impact of image motives on behavior varies with two key features of the choice mechanism: single versus multiple decisions, and certainty versus uncertainty of consequences. Using direct elicitation (DE) versus multiple-price-list (MPL) or equivalently Becker-DeGroot-Marschak (BDM) schemes as exemplars, we characterize how image-seeking inflates prosocial giving. The signaling bias (relative to true preferences) is shown to depend on the interaction between elicitation method and visibility level: it is greater under DE for low image concerns, and greater under MPL/BDM for high ones. We experimentally test the model’s predictions and find the predicted crossing effect. |
| Keywords: | Moral behavior, deontology, utilitarianism, consequentialism, social image, self-image, norms, preference elicitation, multiple price list, experiments |
| JEL: | C91 D01 D62 D64 D78 |
| Date: | 2023–07 |
| URL: | http://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2023_441&r=upt |
| By: | Alexander Braun (University of St. Gallen; Swiss Finance Institute); Niklas Häusle (University of St. Gallen); Paul D. Thistle (University of Nevada, Las Vegas) |
| Abstract: | On-demand insurance is an innovative business model from the InsurTech space, which provides coverage for episodic risks. It makes use of a simple fact in a practical way: People differ in their frequency of exposure as well as the probability of loss. The extra dimension of heterogeneity can be used to screen the insured and shifts the utility-possibility frontier outwards. We provide a sufficient condition under which type-specific full insurance at the actuarially fair price is incentive compatible. We also show that our results hold for various real-world implementations of on-demand insurance. |
| Keywords: | adverse selection, efficiency, risk classification, insurance, insurtech, business models |
| JEL: | D82 D86 G22 |
| Date: | 2023–06 |
| URL: | http://d.repec.org/n?u=RePEc:chf:rpseri:rp2349&r=upt |
| By: | Carlo Fezzi; Mauro Derek J. Ford; Kirsten L.L. Oleson |
| Abstract: | We develop a travel-cost random utility model to estimate the value of recreational ecosystem services provided by more than 170 outdoor sites located on the island of Maui (Hawaii, USA). Particular emphasis is placed on the role of coastal ecosystems by combining recent fine-scale data on coral cover and fish biomass with information on almost 3000 recreation trips taken by Maui’s residents. Our approach is grounded in economic theory and provides estimates that are directly applicable to inform a wide array of spatial planning questions for coastal management. We apply our model to calculate the economic losses caused by the 2014-2015 coral bleaching event, which are in the order of $25M per year. We also identify the areas where coral reef restoration would maximize welfare gains. Impacts can vary up to a factor of 1000 across locations, demonstrating the need to carefully consider such heterogeneity in spatial prioritization. Our simulations also show how access fees can raise funds for financing conservation measures aimed at bolstering coral reefs resilience to climate change. |
| Keywords: | coral reefs, ecosystem services, climate change, recreation, coastal management |
| Date: | 2022 |
| URL: | http://d.repec.org/n?u=RePEc:trn:utwprg:2022/5&r=upt |
| By: | Cristiano Cantore (Sapienza University of Rome); Filippo Ferroni (Chicago Fed); Haroon Mumtaz (Queen Mary University of London); Angeliki Theophilopoulou (Brunel University London) |
| Abstract: | We study the interaction between monetary policy and labor supply decisions at the household level. We uncover evidence of heterogeneous responses and a strong countercyclicality of hours worked in the left tail of the income distribution, following a monetary policy shock in the U.S. and the U.K. That is, while aggregate hours and labor earnings decline, employed individuals at the bottom of the income distribution increase their hours worked in response to an interest rate hike. Moreover, their response is stronger in magnitude relative to other income groups. We rationalize this using a two-agent New-Keynesian (TANK) model where our empirical findings can be replicated with heterogeneity in the marginal utility of consumption and a stronger income effect for the Hand-to-Mouth households. This setup uncovers a novel channel of transmission of monetary policy via inequality generated by the Hand-to-Mouth substitution of leisure for consumption following a negative income shock. Using a quantitative model with both intensive and extensive margin of labor supply that replicates our evidence, we show that this new channel reduces the amplification of monetary policy via inequality generated by the heterogenous behavior of unemployment along the income distribution. |
| Keywords: | Monetary policy, Household Survey, FAVARs, TANK, Hand to Mouth |
| JEL: | E52 E32 C10 |
| Date: | 2023–03 |
| URL: | http://d.repec.org/n?u=RePEc:cfm:wpaper:2308&r=upt |
| By: | Chung I Lu |
| Abstract: | We evaluate benchmark deep reinforcement learning (DRL) algorithms on the task of portfolio optimisation under a simulator. The simulator is based on correlated geometric Brownian motion (GBM) with the Bertsimas-Lo (BL) market impact model. Using the Kelly criterion (log utility) as the objective, we can analytically derive the optimal policy without market impact and use it as an upper bound to measure performance when including market impact. We found that the off-policy algorithms DDPG, TD3 and SAC were unable to learn the right Q function due to the noisy rewards and therefore perform poorly. The on-policy algorithms PPO and A2C, with the use of generalised advantage estimation (GAE), were able to deal with the noise and derive a close to optimal policy. The clipping variant of PPO was found to be important in preventing the policy from deviating from the optimal once converged. In a more challenging environment where we have regime changes in the GBM parameters, we found that PPO, combined with a hidden Markov model (HMM) to learn and predict the regime context, is able to learn different policies adapted to each regime. Overall, we find that the sample complexity of these algorithms is too high, requiring more than 2m steps to learn a good policy in the simplest setting, which is equivalent to almost 8, 000 years of daily prices. |
| Date: | 2023–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2307.07694&r=upt |
| By: | Yiding Feng; Brendan Lucier; Aleksandrs Slivkins |
| Abstract: | We study a game played between advertisers in an online ad platform. The platform sells ad impressions by first-price auction and provides autobidding algorithms that optimize bids on each advertiser's behalf. Each advertiser strategically declares a budget constraint (and possibly a maximum bid) to their autobidder. The chosen constraints define an "inner" budget-pacing game for the autobidders, who compete to maximize the total value received subject to the constraints. Advertiser payoffs in the constraint-choosing "metagame" are determined by the equilibrium reached by the autobidders. Advertisers only specify budgets and linear values to their autobidders, but their true preferences can be more general: we assume only that they have weakly decreasing marginal value for clicks and weakly increasing marginal disutility for spending money. Our main result is that despite this gap between general preferences and simple autobidder constraints, the allocations at equilibrium are approximately efficient. Specifically, at any pure Nash equilibrium of the metagame, the resulting allocation obtains at least half of the liquid welfare of any allocation and this bound is tight. We also obtain a 4-approximation for any mixed Nash equilibrium, and this result extends also to Bayes-Nash equilibria. These results rely on the power to declare budgets: if advertisers can specify only a (linear) value per click but not a budget constraint, the approximation factor at equilibrium can be as bad as linear in the number of advertisers. |
| Date: | 2023–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2307.07374&r=upt |