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on Utility Models and Prospect Theory |
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Issue of 2022‒10‒17
fifteen papers chosen by |
| By: | Larbi Alaoui; Antonio Penta |
| Abstract: | Individuals often attach a special meaning to obtaining a certain goal, and getting past a threshold marks the difference between what they consider a success or a failure. In this paper we take a standard von Neumann-Morgenstern Expected Utility setting with an exogenous reference point that separates success from failure, and define attitudes towards success and failure as features of preferences over lotteries. The distinctive feature of our definitions is that they all concern a local reversal of the decision maker's risk attitude between riskaversion and risk-lovingness across the reference point. Our findings provide a unified view of several well-known models of reference-dependent preferences in economics, finance and psychology, and also include novel representations. Moreover, we introduce orderings over the primitive space of preferences to define different attitudes with which each attitudes can be displayed, and characterize them in terms of the representation, with indices analogous to the well-known Arrow-Pratt index of risk aversion. Our findings shed new light on frequently used notions of reference-dependent preferences, and suggest that new comparative statics analyses be conducted in these settings. Finally, we argue that our framework may prove useful to incorporate, within a standard economic model, behavioral manifestations of personality traits that have received increasing attention within the empirical economics literature. |
| Keywords: | expected utility, loss aversion, aspirations, Risk Aversion, reference-dependence |
| JEL: | D01 D81 |
| Date: | 2022–03 |
| URL: | http://d.repec.org/n?u=RePEc:bge:wpaper:1336&r= |
| By: | Eric Luxenberg; Philipp Schiele; Stephen Boyd |
| Abstract: | We consider the problem of choosing a portfolio that maximizes the cumulative prospect theory (CPT) utility on an empirical distribution of asset returns. We show that while CPT utility is not a concave function of the portfolio weights, it can be expressed as a difference of two functions. The first term is the composition of a convex function with concave arguments and the second term a composition of a convex function with convex arguments. This structure allows us to derive a global lower bound, or minorant, on the CPT utility, which we can use in a minorization-maximization (MM) algorithm for maximizing CPT utility. We further show that the problem is amenable to a simple convex-concave (CC) procedure which iteratively maximizes a local approximation. Both of these methods can handle small and medium size problems, and complex (but convex) portfolio constraints. We also describe a simpler method that scales to larger problems, but handles only simple portfolio constraints. |
| Date: | 2022–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2209.03461&r= |
| By: | Minghao Pan |
| Abstract: | This paper studies relations among axioms on individuals' intertemporal choices under risk. The focus is on Risk Averse over Time Lotteries (RATL), meaning that a fixed prize is preferred to a lottery with the same monetary prize but a random delivery time. Though surveys and lab experiments documented RATL choices, Expected Discounted Utility cannot accommodate any RATL. This paper's contribution is two-fold. First, under a very weak form of Independence, we generalize the incompatibility of RATL with two axioms about intertemporal choices: Stochastic Impatience (SI) and No Future Bias. Next, we prove a representation theorem that gives a class of models satisfying RATL and SI everywhere. This illustrates that there is no fundamental conflict between RATL and SI, and leaves open possibility that RATL behavior is caused by Future Bias. |
| Date: | 2022–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2209.01790&r= |
| By: | Ferran Sancho |
| Abstract: | We reformulate the Stone-Geary utility function to incorporate non-unitary elasticities of substitution. We show that this extended linear expenditure system includes the standard Stone-Geary case but eliminates some of its restrictions. In particular, and most significantly, the proportions of expenditure over leftover income become price responsive under the extended demand system. |
| Keywords: | linear expenditure system, constant elasticity of substitution, calibrated demand functions |
| JEL: | C55 D11 D12 |
| Date: | 2022–03 |
| URL: | http://d.repec.org/n?u=RePEc:bge:wpaper:1328&r= |
| By: | Seungjin Han; Julius Owusu; Youngki Shin |
| Abstract: | In this paper we study treatment assignment rules in the presence of social interaction. We construct an analytical framework under the anonymous interaction assumption, where the decision problem becomes choosing a treatment fraction. We propose a multinomial empirical success (MES) rule that includes the empirical success rule of Manski (2004) as a special case. We investigate the non-asymptotic bounds of the expected utility based on the MES rule. Finally, we prove that the MES rule achieves the asymptotic optimality with the minimax regret criterion. |
| Date: | 2022–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2209.09077&r= |
| By: | Piotr Dworczak (Northwestern University; Group for Research in Applied Economics (GRAPE)) |
| Abstract: | I study a simple equity-efficiency problem: A designer allocates a fixed amount of money to a population of agents differing in privately observed marginal values for money. She can only screen agents by asking them to burn utility (through some socially wasteful activity). I show that giving a lump-sum payment is outperformed by a mechanism with utility burning when the agent with the lowest money-denominated cost of engaging in the wasteful activity has an expected value for money that exceeds the average value by more than a factor of two. |
| JEL: | C78 D47 D61 D63 D82 |
| Date: | 2022 |
| URL: | http://d.repec.org/n?u=RePEc:fme:wpaper:70&r= |
| By: | Erhan Bayraktar; Tao Chen |
| Abstract: | We consider a multi-period stochastic control problem where the multivariate driving stochastic factor of the system has known marginal distributions but uncertain dependence structure. To solve the problem, we propose to implement the nonparametric adaptive robust control framework. We aim to find the optimal control against the worst-case copulae in a sequence of shrinking uncertainty sets which are generated from continuously observing the data. Then, we use a stochastic gradient descent ascent algorithm to numerically handle the corresponding high dimensional dynamic inf-sup optimization problem. We present the numerical results in the context of utility maximization and show that the controller benefits from knowing more information about the uncertain model. |
| Date: | 2022–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2209.04976&r= |
| By: | Krähmer, Daniel (University of Bonn); Strausz, Roland (HU Berlin) |
| Abstract: | We introduce consumers with intrinsic privacy preferences into the monopolistic non-linear pricing model. Next to classical consumers, there is a share of data-sensitive consumers who incur a privacy cost if their purchase reveals information to the monopolist. The monopolist discriminates between privacy types using privacy mechanisms which consist of a direct mechanism and a privacy option, targeting, respectively, classical and data-sensitive consumers. We show that a privacy mechanism is optimal if privacy costs are large and that it yields classical consumers a higher utility than data-sensitive consumers with the same valuation. If, by contrast, privacy preferences are public information, data-sensitive consumers with a low valuation obtain a strictly higher utility than classical consumers. With public privacy preferences, data-sensitive consumers and the monopolist are better off, whereas classical consumers are worse off. Our results are relevant for policy measures that target the data-awareness of consumers, such as the European GDPR. |
| Keywords: | optimal non-linear pricing; privacy; monopolistic screening; |
| Date: | 2021–11–19 |
| URL: | http://d.repec.org/n?u=RePEc:rco:dpaper:301&r= |
| By: | Mel Win Khaw; Ziang Li; Michael Woodford |
| Abstract: | In an experiment that elicits subjects’ willingness to pay (WTP) for the outcome of a lottery, we confirm the fourfold pattern of risk attitudes described by Kahneman and Tversky. In addition, we document a systematic effect of stake sizes on the magnitude and sign of the relative risk premium, holding fixed both the probability that a lottery pays off and the sign of its payoff (gain vs. loss). We further show that in our data, there is a log-linear relationship between the monetary payoff of the lottery and WTP, conditional on the probability of the payoff and its sign. We account quantitatively for this relationship, and the way in which it varies with both the probability and sign of the lottery payoff, in a model in which all departures from risk-neutral bidding are attributed to an optimal adaptation of bidding behaviour to the presence of cognitive noise. Moreover, the cognitive noise required by our hypothesis is consistent with patterns of bias and variability in judgments about numerical magnitudes and probabilities that have been observed in other contexts. |
| Keywords: | prospect theory, fourfold pattern, endogenous precision, cognitive noise |
| JEL: | C91 D03 D81 D87 |
| Date: | 2022 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_9923&r= |
| By: | Mujcic, Redzo (University of Warwick); Powdthavee, Nattavudh (University of Warwick) |
| Abstract: | In a controlled field setting, in which the majority of people in our sample lose more than £90,000 ($120,000), we examine how human beings respond to major financial losses. University ethics boards would not allow this kind of huge-loss phenomenon to be studied with normal social-science experiments. Yet the scientific and practical issues at stake are unusually important ones. In our setting, individuals are handed £100,000 in cash. They then have to make risky decisions. Facing a sequence of seven questions, individuals are required to distribute their cash endowment over a set of possible answers. Participants lose any cash placed on a wrong answer. We find evidence of risk reduction after people suffer a loss in the previous decision round. A prior financial loss of £10,000 is estimated to increase the propensity to fully diversify by 6 percentage points. In terms of proportional losses, a loss of 50% or more of the remaining cash endowment increases diversification rates by approximately 13 percentage points. The fixed-effects panel data estimates are robust to the remaining cash endowment, previous diversification strategy, relative difficulty of questions, the ability level of participants, and other personal traits. The findings support a prospect theory-based model with a coefficient of loss aversion that is increasing in past losses. Our study appears to be the first to be able to calculate systematically how human beings react to enormous and unrecoverable financial losses. |
| Keywords: | risk taking, prior losses, diversification, large stakes, field evidence |
| JEL: | D81 G11 G40 G41 |
| Date: | 2022–09 |
| URL: | http://d.repec.org/n?u=RePEc:iza:izadps:dp15536&r= |
| By: | Freund, L. B.; Lee, H.; Rendahl, P. |
| Abstract: | This paper studies the role of macroeconomic uncertainty in a search-and-matching framework with risk-averse households. Heightened uncertainty about future productivity reduces current economic activity even in the absence of nominal rigidities. A risk-premium mechanism accounts for this result. As future asset prices become more volatile and covary more positively with aggregate consumption, the risk premium rises in the present. The associated downward pressure on current asset values lowers firm entry, making it harder for workers to find jobs and reduces supply. With nominal rigidities the recession is exacerbated, as a more uncertain future reinforces households’ precautionary behavior, which causes demand to contract. Counterfactual analyses using a calibrated model imply that unemployment would rise by less than half as much absent the risk-premium channel. The presence of this mechanism implies that uncertainty shocks are less deflationary than regular demand shocks, nor can they be fully neutralized by monetary policy. |
| Keywords: | inflation, search frictions, Uncertainty, Unemployment |
| JEL: | J64 E21 E32 |
| Date: | 2022–09–08 |
| URL: | http://d.repec.org/n?u=RePEc:cam:camdae:2251&r= |
| By: | Zegners, Dainis (Erasmus University Rotterdam); Sunde, Uwe (LMU Munich); Strittmatter, Anthony (CREST-ENSAE) |
| Abstract: | This paper presents a novel approach to analyze human decision-making that involves comparing the behavior of professional chess players relative to a computational benchmark of cognitively bounded rationality. This benchmark is constructed using algorithms of modern chess engines and allows investigating behavior at the level of individual move-by-move observations, thus representing a natural benchmark for computationally bounded optimization. The analysis delivers novel insights by isolating deviations from this benchmark of bounded rationality as well as their causes and consequences for performance. The findings document the existence of several distinct dimensions of behavioral deviations, which are related to asymmetric positional evaluation in terms of losses and gains, time pressure, fatigue, and complexity. The results also document that deviations from the benchmark do not necessarily entail worse performance. Faster decisions are associated with more frequent deviations from the benchmark, yet they are also associated with better performance. The findings are consistent with an important influence of intuition and experience, thereby shedding new light on the recent debate about computational rationality in cognitive processes. |
| Keywords: | cognitively bounded rationality; benchmark computing; artificial intelligence; decision quality; decision time; |
| JEL: | D01 |
| Date: | 2020–12–22 |
| URL: | http://d.repec.org/n?u=RePEc:rco:dpaper:263&r= |
| By: | Ruodu Wang; Qinyu Wu |
| Abstract: | Quasi-convexity in probabilistic mixtures is a common and useful property in decision analysis. We study a general class of non-monotone mappings, called the generalized rank-dependent functions, which include the preference models of expected utilities, dual utilities, and rank-dependent utilities as special cases, as well as signed Choquet integrals used in risk management. As one of our main results, quasi-convex (in mixtures) signed Choquet integrals precisely include two parts: those that are convex (in mixtures) and the class of scaled quantile-spread mixtures, and this result leads to a full characterization of quasi-convexity for generalized rank-dependent functions. Seven equivalent conditions for quasi-convexity in mixtures are obtained for dual utilities and signed Choquet integrals. We also illustrate a conflict between convexity in mixtures and convexity in risk pooling among constant-additive mappings. |
| Date: | 2022–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2209.03425&r= |
| By: | Alex Centeno; Leidy Garc\'ia |
| Abstract: | The objective of this paper is to identify and analyze the response actions of a set of partially rational players embedded in sub-networks in the context of social interaction and learning. We characterize strategic network formation as a static game of interactions with incomplete information, where players maximize their utility depending on the connections they establish and multiple interdependent actions that permit group-specific parameters of players. It is challenging to apply this type of model to real-life scenarios for two reasons: The computation of the Bayesian Nash Equilibrium is highly demanding and the identification of social influence requires the use of excluded variables that are oftentimes unavailable. Based on the theoretical proposal, we propose a set of simulant equations and discuss the identification of the social interaction effect employing multi-modal network autoregressive. |
| Date: | 2022–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2209.08380&r= |
| By: | Xintong Han (Concordia University and CIREQ, Department of Economics, 1455 Boulevard de Maisonneuve Ouest, Concordia University, Montreal, H3G 1M8, Canada); Shaojia Wang (Concordia University, Department of Economics, 1455 Boulevard de Maisonneuve Ouest, Concordia University, Montreal, H3G 1M8, Canada); Tong Wang (University of Edinburgh, Business School, 29 Buccleuch Pl, Edinburgh EH8 9JS. United Kingdom) |
| Abstract: | Using unique data from a leading Chinese content platform with more than 300,000 users, we propose a structural approach to evaluate the effect of the structure of a referral network on users’ renewal decisions. Referral networks provide essential identification sources, which enable us to embed the expectation of network peers’ behavior into the utility function as an important component to capture the decision variations. We find that these networks play an essential role in users’ renewal decisions, which are significantly and positively associated with the renewal decisions of both referrers and referrals. Our counterfactual analysis has important implications for the referral policies of digital platforms. First, we find that the referral-targeted discount discrimination policy is more effective than the uniform discount policy. More optimistic expectations for referrals’ decisions due to the price discount generate a snowball effect on referral networks, which in turn increases renewal rates. Compared to a uniform discount policy, a more referral-targeted discount policy would significantly increase renewal rates while reducing overall revenue loss. Second, our results highlight the importance of the structure of a referral network. With the same beta index, a high-centrality network implies a reduction in the chain hierarchy, which is detrimental to customer retention. We suggest that an efficient referral network should be highly connected with a lower degree of closeness-based centrality. |
| Keywords: | network structural; renewal decision; referral programs; structural estimation |
| JEL: | C51 L53 L82 |
| Date: | 2022–09 |
| URL: | http://d.repec.org/n?u=RePEc:net:wpaper:2205&r= |