
on Utility Models and Prospect Theory 
By:  Zvi Safra (Warwick Business School; Tel Aviv University); Uzi Segal (Boston College) 
Abstract:  We consider a risk averse decision maker who dislikes ambiguity as in the Ellsberg urns and compare the certainty equivalent of this gamble with the certainty equivalent of the anchoring probabilistic lottery. We deal first with the Choquet EU model and show that un der some conditions on the capacity nu, when independent ambiguous gambles are repeated and the expected value of the anchoring lot tery is zero, the difference between the average ambiguous and risky certainty equivalents converges to zero. When the parallel expected value is positive, we show that if the average certainty equivalent of the risky lottery is nonnegative, then so is the limit of the average value for the ambiguous model. These results do not extend to the maxmin model or to the smooth recursive model. 
Keywords:  Ellsberg urns, repeated ambiguity, repeated risk, Choquet expected utility, maxmin 
JEL:  D81 
Date:  2018–06–15 
URL:  http://d.repec.org/n?u=RePEc:boc:bocoec:954&r=upt 
By:  Roxane Bricet (Université de CergyPontoise, THEMA) 
Abstract:  Most of reallife decision problems are usually characterized by uncertainty regarding the probability distribution of outcomes. This article experimentally investigates individual’s attitude towards partial ambiguity, defined by situations where more or less precise sets of observations are available to the agents. Drawing on Ellsberg’s 2urns experiment, I depart from the classic design and describe both urns by datasets with different degrees of precision. As a result, most subjects behave in conformity with the Expected Utility Hypothesis although a significant proportion of choices can still be interpreted as an expression of nonneutral ambiguity attitude. I calculate an individual score of ambiguitysensitivity which suggests a significant bias towards ambiguityaversion, but weaker than in the related literature. 
Keywords:  Preferences for information precision, Ambiguity, Ellsberg paradox, Experiment. 
JEL:  C91 D81 
Date:  2018 
URL:  http://d.repec.org/n?u=RePEc:ema:worpap:201808&r=upt 
By:  Takehito Masuda; Eungik Lee 
Abstract:  This paper provides experimental evidence of the role of higher order risk attitudes—especially prudence—in prevention behavior. Prudence, under an expected utility framework, increases (decreases) selfprotection effort compared to the risk neutral level when the risk of losing part of an income exists in a future (the same) period. Motivated by these predictions that give the exact test on prudence, an experiment was designed where subjects go through higher order risk attitude elicitation and make a selfprotection decision. In contrast to expected utility theory, the observed efforts are less than the risk neutral level, regardless of the timing of loss. This violation of expected utility predictions could be explained by probability weighting. 
Date:  2018–06 
URL:  http://d.repec.org/n?u=RePEc:dpr:wpaper:1034&r=upt 
By:  Christophe Labreuche (Thales Research & Technology  Palaiseau); Michel Grabisch (Centre d'Economie de la Sorbonne  Paris School of Economics) 
Abstract:  In many MultiCriteria Decision problems, one can construct with the decision maker several reference levels on the attributes such that some decision strategies are conditional on the comparison with these reference levels. The classical models (such as the Choquet integral) cannot represent these preferences. We are then interested in two models. The first one is the Choquet with respect to a pary capacity combined with utility functions, where the pary capacity is obtained from the reference levels. The second one is a specialization of the GeneralizedAdditive Independence (GAI) model, which is discretized to fit with the presence of reference levels. These two models share common properties (monotonicity, continuity, properly weighted, …), but differ on the interpolation means (Lovász extension for the Choquet integral, and multilinear extension for the GAI model). A drawback of the use of the Choquet integral with respect to a pary capacity is that it cannot satisfy decision strategies in each domain bounded by two successive reference levels that are completely independent of one another. We show that this is not the case with the GAI model 
Keywords:  Multiple criteria analysis; Generalized Additive Independence; Choquet integral; reference levels; interpolation 
Date:  2018–03 
URL:  http://d.repec.org/n?u=RePEc:mse:cesdoc:18009&r=upt 
By:  Jerry Tsai; Jessica A. Wachter 
Abstract:  We solve for asset prices in a general affine representativeagent economy with isoelastic recursive utility and rare events. Our novel solution method is exact in two special cases: no preference for early resolution of uncertainty and elasticity of intertemporal substitution equal to one. Our results clarify model properties governed by the elasticity of intertemporal substitution, by risk aversion, and by the preference for early resolution of uncertainty. Finally, we show in a general setting that the linear relation between normaltimes covariances and expected returns need not hold in a model with rare events. 
JEL:  G12 
Date:  2018–05 
URL:  http://d.repec.org/n?u=RePEc:nbr:nberwo:24641&r=upt 
By:  Matteo Brachetta; Claudia Ceci 
Abstract:  In this work we investigate the optimal proportional reinsuranceinvestment strategy of an insurance company which wishes to maximize the expected exponential utility of its terminal wealth in a finite time horizon. Our goal is to extend the classical CramerLundberg model introducing a stochastic factor which affects the intensity of the claims arrival process, described by a Cox process, as well as the insurance and reinsurance premia. Using the classical stochastic control approach based on the HamiltonJacobiBellman equation we characterize the optimal strategy and provide a verification result for the value function via classical solutions of two backward partial differential equations. Existence and uniqueness of these solutions are discussed. Results under various premium calculation principles are illustrated and a new premium calculation rule is proposed in order to get more realistic strategies and to better fit our stochastic factor model. Finally, numerical simulations are performed to obtain sensitivity analyses. 
Date:  2018–06 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1806.01223&r=upt 
By:  Roxane Bricet (Université de CergyPontoise, THEMA) 
Abstract:  This paper presents an experiment designed to measure the effect of information precision on ambiguity attitudes. The Ellsberg’s twourns experiment is adapted so that the subjects are provided with sets of observations informing on the composition of the ambiguous urn. The central feature of the design consists in keeping the frequencies of observations constant across datasets, which allows to isolate the influence of information precision by varying the number of observations. The experimental results suggest that the availability of information does not eliminate Ellsbergtype preferences, since most subjects prefer the risky urn to the ambiguous urn to bet on both colors, but it does not translate into significantly different valuations for the risky and ambiguous prospects. Moreover, I do not find evidence that the increase in information precision is associated with higher valuation of the ambiguous prospect. 
Keywords:  Preferences for information precision, Ambiguity, Ellsberg paradox, Certainty Equivalence, Preference Reversals, Experiment, Prince. 
JEL:  C91 D81 D83 
Date:  2018 
URL:  http://d.repec.org/n?u=RePEc:ema:worpap:201809&r=upt 
By:  Cornel Kaufmann, Tobias Mueller, Andreas Hefti, Stefan Boes 
Abstract:  Choicebased health insurance systems allow individuals to select a health plan that ts their needs. However, bounded rationality and limited attention may lead to suboptimal insurance coverage and higherthanexpected outofpocket payments. In this paper, we study the impact of providing personalized information on health plan choices in a laboratory experiment. We seek to more closely mimic reallife choices by randomly providing an incentivized distraction to some individuals. We nd that providing personalized information signi cantly improves health plan choices. The positive e ect is even larger and longerlasting if individuals are distracted from their original task. In addition to providing decision support, receiving personalized information restores the awareness of the choice setting to a level comparable to the case without distraction thus reducing inertia. Our results indicate that increasing transparency of the health insurance system and providing tailored information can help individuals to make better choices and reduce their outofpocket expenditures. 
Keywords:  health insurance choice; decision under uncertainty; limited attention; information; laboratory experiment 
JEL:  I13 D83 C91 
Date:  2018–03 
URL:  http://d.repec.org/n?u=RePEc:ube:dpvwib:dp1808&r=upt 
By:  Thai Nguyen; Mitja Stadje 
Abstract:  This paper studies a VaRregulated optimal portfolio problem of the equity holder of a participating life insurance contract. In a complete market setting the optimal solution is given explicitly for contracts with mortality risk using a martingale approach for constrained nonconcave optimizations. We show that regulatory VaR constraints for participating insurance contracts lead to more prudent investment than the unconstrained solution in loss states. This result is contrary to the situation where the insurer maximizes the utility of the total wealth of the company (without distinguishing between equity and policy holders), in which case a VaR constraint may induce the insurer to take excessive risk leading to higher losses than in the case of no regulation, see Basak and Shapiro (2001). Furthermore, importantly for regulator we observe that for participating insurance contracts both relatively small or relatively large policyholder contributions yield rather risky and volatile strategies. Finally, we also discuss the regulatory effect of a portfolio insurance (PI), and analyze different choices for the parameters of the participating contract numerically. 
Date:  2018–05 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1805.09068&r=upt 
By:  Roxane Bricet (Université de CergyPontoise, THEMA) 
Abstract:  In this article, I propose an experimental design to measure the value of instrumental information in a modelfree setup. In particular, this study provides operating instructions to test Blackwell’s ranking of informative structures under risk and under ambiguity. Drawing on Ellsberg’s twocolor thought experiment, the subject faces three different types of choice situations: simple risk, compound risk and ambiguity. The original experiment is modified by enabling the agent to observe random draws with replacement so that he can learn about the composition of the urns. The proposed design allows to estimate the value of signals that differ in their informativeness and how it relates to ambiguity attitudes. 
Keywords:  Value of Information, Ambiguity, Blackwell’s theorem, Reduction of Compound Lotteries, Ellsberg paradox, Experiment, Prince. 
JEL:  C91 D81 D83 
Date:  2018 
URL:  http://d.repec.org/n?u=RePEc:ema:worpap:201810&r=upt 
By:  Victor Stango (University of CaliforniaDavis); Joanne Yoong (University of Southern California, National University of Singapore, and the London School of Hygiene and Tropical Medicine); Jonathan Zinman (Dartmouth College and NBER) 
Abstract:  Behavioral economics lacks empirical evidence on some foundational questions. We adapt standard elicitation methods to measure multiple behavioral factors per person in a representative U.S. sample, along with financial condition, cognitive skills, financial literacy, classical preferences, and demographics. Individually, behavioral factors are prevalent, distinct from other decision inputs, and correlate negatively with financial outcomes in richlyconditioned regressions. Conditioning further on other Bfactors does not change the results, validating common practice of modeling Bfactors separately. Corrections for low task/survey effort modestly strengthen the results. Our findings provide bedrock empirical foundations for behavioral economics, and offer methodological guidance for research designs. 
Date:  2018–04 
URL:  http://d.repec.org/n?u=RePEc:mrr:papers:wp378&r=upt 
By:  Stark, Oded 
Abstract:  We study the relative risk aversion of an individual with particular social preferences: his wellbeing is influenced by his relative wealth, and by how concerned he is about having low relative wealth. Holding constant the individual's absolute wealth, we obtain two results. First, if the individual's level of concern about low relative wealth does not change, the individual becomes more risk averse when he rises in the wealth hierarchy. Second, if the individual's level of concern about low relative wealth intensifies when he rises in the wealth hierarchy and if, in precise sense, this intensification is strong enough, then the individual becomes less risk averse: the individual's desire to advance further in the wealth hierarchy is more important to him than possibly missing out on a better rank. 
Keywords:  Relative risk aversion,Wealth rank,Concern about low relative wealth 
JEL:  D31 D81 G11 
Date:  2018 
URL:  http://d.repec.org/n?u=RePEc:zbw:tuewef:105&r=upt 
By:  J\"orn Sass; Dorothee Westphal; Ralf Wunderlich 
Abstract:  This paper investigates a financial market where returns depend on an unobservable Gaussian drift process. While the observation of returns yields information about the underlying drift, we also incorporate discretetime expert opinions as an external source of information. For estimating the hidden drift it is crucial to consider the conditional distribution of the drift given the available observations, the socalled filter. For an investor observing both the return process and the discretetime expert opinions, we investigate in detail the asymptotic behavior of the filter as the frequency of the arrival of expert opinions tends to infinity. In our setting, a higher frequency of expert opinions comes at the cost of accuracy, meaning that as the frequency of expert opinions increases, the variance of expert opinions becomes larger. We consider a model where information dates are deterministic and equidistant and another model where the information dates arrive randomly as the jump times of a Poisson process. In both cases we derive limit theorems stating that the information obtained from observing the discretetime expert opinions is asymptotically the same as that from observing a certain diffusion process which can be interpreted as a continuoustime expert. We use these limit theorems to derive socalled diffusion approximations of the filter for highfrequency discretetime expert opinions. They allow for simplified approximate solutions of utility maximization problems since the convergence of the filter carries over to the convergence of the value function for logarithmic utility. 
Date:  2018–07 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1807.00568&r=upt 
By:  Wing Fung Chong; Gechun Liang 
Abstract:  This paper solves the optimal investment and consumption strategies for an ambiguityaverse agent in an incomplete financial market. The agent seeks her best and robust strategies via optimizing her robust forward investment and consumption preferences. The market incompleteness arises from investment constraints of the agent. Her robust forward preferences and the associated optimal strategies are represented via infinite horizon BSDEs. 
Date:  2018–07 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1807.01186&r=upt 
By:  Christian Alcocer; Thomas D. Jeitschko; Thomas D. Jeitschko 
Abstract:  We postulate a new behavioral bias in how people play mixed strategies by proposing the existence of simple players who lack strategic depth; in a sense, they are the simplest possible agents that do not directly contradict the economic principle of utility maximization. We deÖne them as those who, when indi§erent between choices, follow a simple ruleofthumb and assign a predetermined probability to each. We show that if they play 2 2 games, an equilibrium generally fails to exist. However, under random matching within populations with some proportion of simple players, equilibrium is restored and is indistinguishable from Nash equilibria in games with unrestricted strategy choices, as long as the percentage of simple mixers is small enough. As such, players are unable to take advantage of the presence of simple mixers, and simple mixers do no worse than more sophisticated players. 
Keywords:  Behavioral, Bounded Rationality, Mixed Equilibria 
JEL:  C72 D03 D83 
Date:  2018–01–23 
URL:  http://d.repec.org/n?u=RePEc:col:000416:016344&r=upt 
By:  JeanBaptiste Michau; Yoshiyasu Ono; Matthias Schlegl 
Abstract:  We consider a neoclassical economy where households derive utility from holding wealth. We show that, under some conditions, there can be rational bubbles. Hence, we provide a microfoundation for bubbles that relies on a frictionless infinitehorizon economy without any heterogeneity across households. While our bubbly equilibria are very similar to those obtained by Tirole (1985) in an overlapping generation economy, the underlying economics is different. Turning to public debt, we show that Ponzi schemes can be sustainable. Hence, in general, the limit on the accumulation of public debt by the government is not given by its noPonzi condition but, instead, by the representative household's transversality condition. The Ricardian equivalence must hold in any of our equilibria. Finally, in the presence of money, the real equilibrium structure of the economy remains unchanged. We carefully investigate the effects of helicopter drops of money on the possibility of Ponzi schemes and of speculative hyperinflation or deflation. 
Date:  2018–06 
URL:  http://d.repec.org/n?u=RePEc:dpr:wpaper:1035&r=upt 