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on Utility Models and Prospect Theory |
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Issue of 2020‒05‒04
sixteen papers chosen by |
| By: | Giuseppe Ferro (ETH Zürich - Department of Management, Technology, and Economics (D-MTEC)); Didier Sornette (ETH Zürich - Department of Management, Technology, and Economics (D-MTEC); Swiss Finance Institute) |
| Abstract: | Humans are notoriously bad at understanding probabilities, exhibiting a host of biases and distortions that are context dependent. This has serious consequences on how we assess risks and make decisions. Several theories have been developed to replace the normative rational expectation theory at the foundation of economics. These approaches essentially assume that (subjective) probabilities weight multiplicatively the utilities of the alternatives offered to the decision maker, although evidence suggest that probability weights and utilities are often not separable in the mind of the decision maker. In this context, we introduce a simple and efficient framework on how to describe the inherently probabilistic human decision-making process, based on a representation of the deliberation activity leading to a choice through stochastic processes, the simplest of which is a random walk. Our model leads naturally to the hypothesis that probabilities and utilities are entangled dual characteristics of the real human decision making process. It derives two previously postulated features of prospect theory (Kahneman and Tversky, 1979): the inverse S-shaped subjective probability as a function of the objective probability and risk-seeking behaviour in the loss domain. It also predicts observed violations of stochastic dominance (Birnbaum and Navarrete, 1998) while it does not when the dominance is “evident”. Our theory, which offers many more predictions for future tests, has strong implications for psychology, economics and artificial intelligence. |
| Keywords: | stochastic decision theory, duality of probability and value, subjective probability, risk-seeking behaviour, stochastic dominance |
| JEL: | A12 C44 D81 |
| Date: | 2020–04 |
| URL: | http://d.repec.org/n?u=RePEc:chf:rpseri:rp2025&r=all |
| By: | Jose Apesteguia; Miguel Ángel Ballester |
| Abstract: | We study random utility models in which heterogeneity of preferences is modeled using an ordered collection of utilities, or types. The paper shows that these models are particularly amenable when combined with domains in which the alternatives of each decision problem are ordered by the structure of the types. We enhance their applicability by: (i) working with arbitrary domains composed of such decision problems, i.e., we do not need to assume any particularly rich data domain, and (ii) making no parametric assumption, i.e., we do not need to formulate any particular assumption on the distribution over the collection of types. We characterize the model by way of two simple properties and show the applicability of our result in settings involving decisions under risk. We also propose a goodness-of- t measure for the model and prove the strong consistency of extremum estimators defined upon it. We conclude by applying the model to a dataset on lottery choices. |
| Keywords: | random utility model, ordered type-dependent utilities, arbitrary domains, non-parametric, goodness-of-fit, extremum estimators, decision under risk |
| JEL: | C00 D00 |
| Date: | 2020–04 |
| URL: | http://d.repec.org/n?u=RePEc:bge:wpaper:1176&r=all |
| By: | Gänßle, Sophia; Kunz-Kaltenhaeuser, Philipp |
| Abstract: | Behavioral patterns in media consumption are changing. With the upcoming of video-on-demand platforms, so-called "binge-watching" gained broad awareness. To the best of our knowledge, this is the first economic analysis explicitly on binge-watching. We approach the phenomenon by arguing that it follows fundamental patterns of addictive behavior. By applying concepts of rational addiction and behavioral economics, we derive (i) a theoretical understanding of binging-watching behavior and (ii) factors increasing the likelihood of binging, especially with modern technologies and digital media services. The decision to binge depends on individual factors such as the accumulation rate of consumption capital (speed of learning and acquiring knowledge), opportunity costs, and the expected value of consumption. Consumption capital in the form of specific knowledge positively influences marginal utility. Moreover, binge-watching is not specific to online streaming services (video-on-demand), but modern platforms facilitate certain factors which increase the consumers' engagement. Non-linear, self-organized video scheduling and a single narrative (coherent plot) increase the likelihood for con-sumers to binge. |
| Keywords: | binge watching,video on demand,television,streaming,consumption capital,behavioural economics,media economics |
| JEL: | D03 D11 D90 L82 Z10 |
| Date: | 2020 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:tuiedp:138&r=all |
| By: | Soham R. Phade; Venkat Anantharam |
| Abstract: | The betweenness property of preference relations states that a probability mixture of two lotteries should lie between them in preference. It is a weakened form of the independence property and hence satisfied in expected utility theory (EUT). Experimental violations of betweenness are well-documented and several preference theories, notably cumulative prospect theory (CPT), do not satisfy betweenness. We prove that CPT preferences satisfy betweenness if and only if they conform with EUT preferences. In game theory, lack of betweenness in the players' preference relations makes it essential to distinguish between the two interpretations of a mixed action by a player - conscious randomizations by the player and the uncertainty in the beliefs of the opponents. We elaborate on this distinction and study its implication for the definition of Nash equilibrium. This results in four different notions of equilibrium, with pure and mixed action Nash equilibrium being two of them. We dub the other two pure and mixed black-box strategy Nash equilibrium respectively. We resolve the issue of existence of such equilibria and examine how these different notions of equilibrium compare with each other. |
| Date: | 2020–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2004.09592&r=all |
| By: | Tanmay Sen; Ritwik Bhattacharya; Biswabrata Pradhan; Yogesh Mani Tripathi |
| Abstract: | Determination of an appropriate warranty length for the lifetime of the product is an important issue to the manufacturer. In this article, optimal warranty length of the product for the combined free replacement and the pro-rata warranty policy is computed based on the Type-II unified hybrid censored data. A non-linear pro-rata warranty policy is proposed in this context. The optimal warranty length is obtained by maximizing an expected utility function. The expectation is taken with respect to the posterior predictive model for the time-to-failure data. It is observed that the non-linear pro-rata warranty policy gives a larger warranty length with maximum profit as compared to linear warranty policy. Finally, a real-data set is analyzed in order to illustrate the advantage of using non-linear pro-rata warranty policy. |
| Date: | 2020–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2004.08533&r=all |
| By: | Christina Letsou (Boston College); Shlomo Naeh (Hebrew University of Jerusalem); Uzi Segal (Boston College) |
| Abstract: | A common procedure for selecting people is to have them draw balls from an urn in turn. Modern and ancient stories suggest that such lotteries may be viewed by the individuals as “unfair.” We compare this procedure with several alternatives. They all give individuals equal chance of being selected, but have different structures. We an- alyze these procedures as multistage lotteries. In line with previous literature, our analysis is based on the observation that multistage lotteries are not considered indifferent to their probabilistic one-stage representations. We use a non-expected utility model and show that individuals have preferences over the different procedures. |
| Keywords: | Fair lotteries, non-expected utility, multi-stage lotteries |
| JEL: | D63 |
| Date: | 2020–04–28 |
| URL: | http://d.repec.org/n?u=RePEc:boc:bocoec:998&r=all |
| By: | Michel Beine; Gary Charness; Arnaud Dupuy; Majlinda Joxhe |
| Abstract: | We conduct a survey and incentivized lab-in-the-field experimental tasks in Tirana, Albania. While the original purpose of our study was to examine whether and how deep parameters such as time and risk preferences affect the intention to migrate, our study was transformed into a natural experiment owing to two large earthquakes that shook the Tirana area during our data-collection period. These events provide us with a rare opportunity to gather evidence (including a pre-earthquake control) on the effect of natural disasters on time and risk preferences. We find unambiguous effects towards more risk aversion and impatience for affected individuals. Moreover, as it turns out, the second earthquake amplified the effect of the first one, suggesting that experiences cumulate in their influence on these preferences. |
| Keywords: | time preferences, risk preferences, natural disaster, Albania, migration |
| JEL: | B49 C90 D91 F22 |
| Date: | 2020 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_8187&r=all |
| By: | Howard Kunreuther; Mark Pauly |
| Abstract: | Do consumers show a strong bias toward low deductible insurance plans, as many field studies imply? This paper reports on a controlled experiment intended to see whether subjects have a predisposition toward such plans and whether that preference is consistent when their default plan and premiums are changed. Subjects were presented with a scenario where they had to make a decision on whether to purchase a plan with a low deductible (LD) or high deductible (HD) when faced with an illness having a specified probability and cost. Participants had to choose between these plans in two rounds with the identical risk of an illness and specified premiums. If their default option was an LD plan in Round 1, then it was an HD plan in Round 2. The experiment did not show a strong bias toward low deductible health plans. Only slightly more than half of the respondents chose an LD plan even when it was optimal for them to do so. When faced with a default option that was switched in Round 2, 58% of the respondents chose the same plan as they did in Round 1, implying that some but not all subjects resisted the default option in their decision process. Subject choices were correlated with their responses to questions about risk aversion and a desire for peace of mind. |
| JEL: | C90 C91 D03 D12 D3 D81 G22 I11 I18 |
| Date: | 2020–04 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:26994&r=all |
| By: | John Y. Campbell; Roman Sigalov |
| Abstract: | We show that reaching for yield—a tendency to take more risk when the real interest rate declines while the risk premium remains constant—results from imposing a sustainable spending constraint on an otherwise standard infinitely lived investor with power utility. This is true for two alternative versions of the constraint which make wealth and consumption follow martingales in levels or in logs, respectively. Reaching for yield intensifies when the interest rate is initially low, helping to explain the salience of the topic in the current low-rate environment. The sustainable spending constraint also affects the response of risktaking to a change in the risk premium, which can even be negative when the riskless interest rate is sufficiently low. In a variant of the model where the sustainable spending constraint is formulated in nominal terms, low inflation also encourages risktaking. |
| JEL: | E43 G11 |
| Date: | 2020–04 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:27025&r=all |
| By: | Sergio Firpo; Antonio F. Galvao; Martyna Kobus; Thomas Parker; Pedro Rosa-Dias |
| Abstract: | In this paper we develop theoretical criteria and econometric methods to rank policy interventions in terms of welfare when individuals are loss-averse. The new criterion for "loss aversion-sensitive dominance" defines a weak partial ordering of the distributions of policy-induced gains and losses. It applies to the class of welfare functions which model individual preferences with non-decreasing and loss-averse attitudes towards changes in outcomes. We also develop new statistical methods to test loss aversion-sensitive dominance in practice, using nonparametric plug-in estimates. We establish the limiting distributions of uniform test statistics by showing that they are directionally differentiable. This implies that inference can be conducted by a special resampling procedure. Since point-identification of the distribution of policy-induced gains and losses may require very strong assumptions, we also extend comparison criteria, test statistics, and resampling procedures to the partially-identified case. Finally, we illustrate our methods with an empirical application to welfare comparison of two income support programs. |
| Date: | 2020–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2004.08468&r=all |
| By: | Mogens Fosgerau; Dennis Kristensen |
| Abstract: | We establish nonparametric identification in a class of so-called index models using a novel approach that relies on general topological results. Our proof strategy requires substantially weaker conditions on the functions and distributions characterizing the model compared to existing strategies; in particular, it does not require any large support conditions on the regressors of our model. We apply the general identification result to additive random utility and competing risk models. |
| Date: | 2020–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2004.07900&r=all |
| By: | Chenxu Li (Peking University - Guanghua School of Management); O. Scaillet (University of Geneva GSEM and GFRI; Swiss Finance Institute; University of Geneva - Research Center for Statistics); Yiwen Shen (Columbia Business School - Decision Risk and Operations) |
| Abstract: | This paper establishes a new decomposition of optimal dynamic portfolio choice under general incomplete-market diffusion models by disentangling the fundamental impacts on optimal policy from market incompleteness and flexible wealth-dependent utilities. We derive explicit dynamics of the components for the optimal policy, and obtain an equation system for solving the shadow price of market incompleteness, which is found to be dependent on both market state and wealth level. We identify a new important hedge component for non-myopic investors to hedge the uncertainty in shadow price due to variation in wealth level. As an application, we establish and compare the decompositions of optimal policy under general models with the prevalent HARA and CRRA utilities. Under nonrandom but possibly time-varying interest rate, we solve in closed-form the HARA policy as a combination of a bond holding scheme and a corresponding CRRA strategy. Finally, we develop a simulation method to implement the decomposition of optimal policy under the general incomplete market setting, whereas existing approaches remain elusive. |
| Keywords: | optimal portfolio choice, decomposition, incomplete market, wealth-dependent utility, closed-form |
| JEL: | C61 C63 G11 |
| Date: | 2020–04 |
| URL: | http://d.repec.org/n?u=RePEc:chf:rpseri:rp2022&r=all |
| By: | Kerstin Bernoth; Jürgen von Hagen; Casper G. de Vries |
| Abstract: | The use of futures exchange contracts instead of forwards completes the maturity spectrum of the correlation between the spot yield and the premium. We find that the forward premium puzzle (FFP) depends significantly on the maturity horizon of the futures contract and the choice of sampling period. The FFP appears to be a pre-crisis phenomenon and is only observed for maturities longer than about one month. When examining whether the observed excess returns of futures contracts represent a fair compensation for currency risk, we find that non-durable consumption risk and market risk can explain excess currency returns. But only in the pre-crisis period and when the maturity of the assets is longer than about three months. |
| Keywords: | Forward premium puzzle, uncovered interest parity, futures rates, risk premium, currency excess returns, capital asset pricing model |
| JEL: | F31 F37 G12 G13 G15 |
| Date: | 2020 |
| URL: | http://d.repec.org/n?u=RePEc:diw:diwwpp:dp1866&r=all |
| By: | Wei Wei; Asger Lunde |
| Abstract: | We propose a multi-factor model and an estimation method based on particle MCMC to identify risk factors in electricity prices. Our model identifies long-run prices, shortrun deviations, and spikes as three main risk factors in electricity spot prices. Under our model, different risk factors have distinct impacts on futures prices and can carry different risk premia. We generalize the Fama-French regressions to analyze properties of true risk premia. We show that model specification plays an important role in detecting time varying risk premia. Using spot and futures prices in the Germany/Austria market, we demonstrate that our proposed model surpasses alternative models that have less risk factors in forecasting spot prices and in detecting time varying risk premia. |
| Keywords: | Risk factors, risk premia, futures, particle filter, MCMC. |
| JEL: | C51 G13 Q4 |
| Date: | 2020 |
| URL: | http://d.repec.org/n?u=RePEc:msh:ebswps:2020-10&r=all |
| By: | Peter A. Streufert |
| Abstract: | This paper develops the category $\mathbf{NCG}$. Its objects are node-and-choice games, which include essentially all extensive-form games. Its morphisms allow arbitrary transformations of a game's nodes, choices, and players, as well as monotonic transformations of the utility functions of the game's players. Among the morphisms are subgame inclusions. Several characterizations and numerous properties of the isomorphisms are derived. Also, the game-theoretic concepts of no-absentmindedness, perfect-information, and (pure-strategy) Nash-equilibrium are shown to be isomorphically invariant. Finally, full subcategories are defined for choice-sequence games and choice-set games, and relationships among these two subcategories and $\mathbf{NCG}$ itself are expressed and derived via isomorphic inclusions and equivalences. |
| Date: | 2020–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2004.11196&r=all |
| By: | Stefania Minardi (Economics and Decision Sciences Department, HEC Paris); Andrei Savochkin (New Economic School) |
| Abstract: | A consumption event is memorable if the memory of it affects well-being at times after the material consumption. We develop an axiomatic model of memorable consumption in a dynamic setting. Preferences are represented by the present value of the sum of utilities derived at each date from the current consumption and from recollecting the past. Our model accommodates wellknown phenomena in psychology, such as the peak-end rule, duration neglect, and adaptation trends. We provide foundations for a prominent special case of memory that has the Markovian property. The model is illustrated in application to life-cycle consumption-savings decisions and asset pricing. |
| Date: | 2019–10–08 |
| URL: | http://d.repec.org/n?u=RePEc:abo:neswpt:w0255&r=all |