nep-upt New Economics Papers
on Utility Models and Prospect Theory
Issue of 2011‒12‒19
thirteen papers chosen by
Alexander Harin
Modern University for the Humanities

  1. One Theory For Two Risk Premia By Emmanuelle GABILLON (GREThA, CNRS, UMR 5113)
  2. Stochastic Dominance and Nonparametric Comparative Revealed Risk Aversion By Jan Heufer
  3. On the stability of the CRRA utility under high degrees of uncertainty By D Peel; I Paya; T M Niguez; J Perote
  4. Higher-Order Risk Preferences – Consequences for Test and Treatment Thresholds and Optimal Cutoffs By Stefan Felder; Thomas Mayrhofer
  5. Reference dependent ambiguity aversion: theory and experiment By Qiu, Jianying; Weitzel, Utz
  7. Entrepreneurial Choice and Knightian Uncertainty with Borrowing Constraints By Takanori Adachi; Takao Asano
  8. Psychophysical interpretation for utility measures By He, Yuqing
  9. Utility-based Forecast Evaluation with Multiple Decision Rules and a New Maxmin Rule By Manuel Lukas
  11. On the game interpretation of a shadow price process in utility optimization problems under transaction costs By Dmitry B. Rokhlin
  12. Utility Maximization with Addictive Consumption Habit Formation in Incomplete Semimartingale Markets By Xiang Yu
  13. The variance risk premium around the world By Juan M. Londono

  1. By: Emmanuelle GABILLON (GREThA, CNRS, UMR 5113)
    Abstract: Generally, in the standard presentation of the expected utility model, the risk premium represents how much a risk-averse decision maker is ready to pay to have a risk eliminated. Here, however, we introduce a different risk premium: how much should a risk (which could be the return on a financial asset) yield to be acceptable to a risk-averse decision maker. Although our risk premium is derived from the Pratt bid price, it should not be confused with it: the Pratt bid price represents the monetary compensation of a risk. The standard risk premium refers to risk-avoidance; our risk premium, however, refers to risk-taking. We then reanalyse the main results concerning risk aversion under expected utility using this risk premium tool and deduce its main properties.
    Keywords: choices under uncertainty, expected utility, risk aversion, risk premium.
    JEL: D81
    Date: 2011
  2. By: Jan Heufer
    Abstract: It is shown how to test revealed preference data on choices under uncertainty for consistency with first and second order stochastic dominance (FSD or SSD). The axiom derived for SSD is a necessary and sufficient condition for risk aversion. If an investor is risk averse, stochastic dominance relations can be combined with revealed preference relations to recover a larger part of an investor‘s preference. Interpersonal comparison between investors can be based on intersections of revealed preferred and worse sets. Using a variant of Yaari‘s (1969) defi nition of “more risk averse than”, it is shown that it is sufficient to compare only the revealed preference relations of two investors. This makes the approach operational given a fi nite set of observations. The central rationalisability theorem provides strong support for this approach to comparative risk aversion. The entire analysis is kept completely nonparametric and can be used as an alternative or complement to parametric approaches and as a robustness check. The approach is illustrated with an application to experimental data of by Choi et al. (2007). Most subjects come close to SSD-rationality, and most subjects are comparable with each other. The distribution of risk attitudes in the population can be described by comparing subjects‘ choices with any given preference, which is also illustrated.
    Keywords: Comparative risk aversion; experimental economics; induced budget experiments; interpersonal comparison; nonparametric analysis; portfolio choice; revealed preference; risk preference
    JEL: C14 C91 D11 D12
    Date: 2011–11
  3. By: D Peel; I Paya; T M Niguez; J Perote
    Abstract: Economic growth models under uncertainty and rational agents with CRRA utility have been shown to provide quite fragile explanations of consumers.choice as equlib- rium comsumption paths (expected utility) are drastically dependant on distributional assumptions. We show that assuming a SNP distribution for random consumption provides stability to general equilibrium models as expected utility exists for any value of the marginal rate of substitution over time.
    Date: 2011
  4. By: Stefan Felder; Thomas Mayrhofer
    Abstract: Higher-order risk attitudes include risk aversion, prudence, and temperance. This paper analyzes the effects of such preferences on medical test and treatment decisions, represented either by test and treatment thresholds or – if the test characteristics are endogenous – by the optimal cutoff value for testing. For a risk-averse decision maker, treatment is a risk reducing strategy since it prevents the low health outcome that forgoing treatment yields in the sick state. As compared to risk neutrality, risk aversion thus reduces both the test and the treatment threshold and decreases the optimal cutoff. Prudence is relevant if a comorbidity risk applies in the sick state. It leads to even lower thresholds and a lower optimal cutoff. Finally, temperance plays a role if the comorbidity risk is left-skewed. It lowers the thresholds and the optimal cutoff even further. These findings suggest that diagnostics in low prevalence settings (e.g. screening) are considered more beneficial when higher-order risk preferences are taken into account.
    Keywords: Medical decision making; diagnostic risk; test and treatment thresholds; optimal cutoff; risk aversion; prudence
    JEL: D81 I10
    Date: 2011–10
  5. By: Qiu, Jianying; Weitzel, Utz
    Abstract: In standard models of ambiguity, the evaluation of an ambiguous asset, as of a risky asset, is considered as an independent process. In this process only information directly pertaining to the ambiguous asset is used. These models face significant challenges from the finding that ambiguity aversion is more pronounced when an ambiguous asset is evaluated alongside a risky asset than in isolation. To explain this phenomenon, we developed a theoretical model based on reference dependence in probabilities. According to this model, individuals (1) form subjective beliefs on the potential winning probability of the ambiguous asset; (2) use the winning probability of the (simultaneously presented) risky asset as a reference point to evaluate the potential winning probabilities of the ambiguous asset; (3) code potential winning probabilities of the ambiguous asset that are greater than the reference point as gains and those that are smaller than the reference point as losses; (4) weight losses in probability heavier than gains in probability. We tested the crucial assumption, reference dependence in probabilities, in an experiment and found supporting evidence.
    Keywords: Ambiguity Aversion, Reference Point, Comparison, Experiment
    JEL: G1 C9
    Date: 2011–11–01
  6. By: Stefano D'Addona (University of Roma Tre); Frode Brevik (Free University Amsterdam)
    Abstract: We document an unpleasant feature of Epstein-Zin preferences in a stylized model economy of the long-run risk type now widespread in Asset Pricing: Agents with preference parameters commonly described as indicating a "preference for early resolution of uncertainty" achieve higher utility levels if they can commit to ignoring information on the state of the business cycle. For parameter choices similar to those used to explain asset prices, an agent can achieve utility gains equivalent to a more than 40 % increase in life-time consumption by committing to ignore information on the trend growth rate of the endowment good. We show that opting for such a coarser information set can be implemented and supported as an equilibrium strategy.
    Keywords: Recursive preferences; Epstein-Zin preferences; Uncertainty aversion; Information processing; Time inconsistency
    JEL: D83 D84 E32
    Date: 2011
  7. By: Takanori Adachi (School of Economics, Nagoya University); Takao Asano (Faculty of Economics, Okayama University)
    Abstract: This paper studies the effects of Knightian uncertainty, or ambiguity, on entrepreneurial choice. By distinguishing between risk and ambiguity, we first show that ambiguity aversion makes it less likely that an individual will become an entrepreneur. It is also shown that an increase in ambiguity unambiguously reduces the amount of investment. In the presence of borrowing constraints, the less ambiguity averse is the individual, the more likely is his or her investment to be constrained. More importantly, constrained wage workers, who would become entrepreneurs in the absence of credit market imperfection, emerge if and only if the market wage is high enough. These individuals are characterized by an intermediate degree of ambiguity aversion. When interpreting these constrained wage workers as managerial and professional workers, our model predicts the rise of such workers in the process of economic development.
    Keywords: Entrepreneurship, Knightian Uncertainty, Risk, Borrowing Constraints
    JEL: L26 D8
    Date: 2011–12
  8. By: He, Yuqing
    Abstract: The paper explores utility measures by combining experiments with mathematical derivations in psychophysics paradigm. The analysis on ultimatum game experiment reveals an evidence for utility threshold and thus supports Bernoulli's utility logarithmic law. Both experimental results and theoretical derivations show that the logarithmic law is suitable for the description of commodity choice and the power law for risk choice. The further mathematical demonstration indicates the logarithmic law for utility scaling to be a Klein-Rubin utility function, a utility function well defined in microeconomics. Based on this, the experimental utility measure is connected with the econometric model Linear Expenditure System, and presents an experimental procedure for testing the utility maximization hypothesis, which will remove a long unsettled perplexity in a fundamental stone of economics since Gossen proposed it in 1854. --
    Keywords: Psychophysics,ultimatum game,utility function,logarithmic law,power law
    JEL: A12 D01
    Date: 2011
  9. By: Manuel Lukas (Aarhus University and CREATES)
    Abstract: In this paper we generalize the existing approach to utility-based evaluation of density forecast models by allowing for multiple decision rules. In the generalized approach forecast models and decision rules can only be evaluated jointly. We show how to conduct the joint evaluation and explore to which extent conclusions about either forecast models or decision rules are possible. As a specic decision rule we introduce a Gilboa-Schmeidler (1989) type multiple-prior maxmin decision rule, where we use the model condence set of Hansen, Lunde, and Nason (2011) as priors. In an empirical application, the density forecasts of ve GARCH-type models are combined with this maxmin rule and other decision rules for static portfolio choice with daily data on the S&P500.
    Keywords: Decision rules, forecast evaluation and comparison, maxmin, ambiguity aversion, portfolio choice.
    JEL: C44 C53 D81 G11
    Date: 2011–11–26
  10. By: Amanda Stathopoulos (University of Trieste); Stephane Hess (University of Leeds)
    Abstract: In contrast with expected utility theory, empirical findings indicate that decisionmakers are sensitive to departures from reference points rather than states. Several tests of the reference-dependent preference framework have been carried out in experimental economics, and to a smaller extent in a choice modelling setting, to date. However, these empirical applications have generally focussed on a single behavioural phenomenon using uniform modelling approaches. This paper aims to broaden existing work by presenting a multi-attribute framework, allowing contemporarily for gain-loss asymmetry, non-linearity and testing for several possible reference points. The framework is tested in the context of commuter choices and reveals important gains in model fit and further insights into behaviour compared to standard modelling approaches, including substantial impacts on implied welfare measures.
    Keywords: Choice modeling, discrete choice experiment, reference effects, non-linearity, gain/loss deviations, commuting
    JEL: C25 C9 D03 R49
    Date: 2011
  11. By: Dmitry B. Rokhlin
    Abstract: To any utility maximization problem under transaction costs one can assign a frictionless model with a price process $S^*$, lying in the bid/ask price interlval $[\underline S, \bar{S}]$. Such process $S^*$ is called a \emph{shadow price} if it provides the same optimal utility value as in the original model with bid-ask spread. We call $S^*$ a \emph{generalized shadow price} if the above property is true for the \emph{relaxed} utility function in the frictionless model. This relaxation is defined as the lower semicontinuous envelope of the original utility, considered as a function on the set $[\underline S, \bar{S}]$, equipped with some natural weak topology. We prove the existence of a generalized shadow price under rather weak assumptions and mark its relation to a saddle point of the trader/market zero-sum game, determined by the relaxed utility function. The relation of the notion of a shadow price to its generalization is illustrated by several examples. Also, we briefly discuss the interpretation of shadow prices via Lagrange duality.
    Date: 2011–12
  12. By: Xiang Yu
    Abstract: This paper studies the problem of continuous time utility maximization of consumption together with addictive habit formation in general incomplete semimartingale financial markets. By introducing the auxiliary state processes and the modified dual space, we embed our original problem into an auxiliary time separable utility maximization problem with the shadow random endowment. We establish existence and uniqueness of the optimal solution using convex duality approach on the product space by defining the primal value function both on the initial wealth and initial habit. We also provide market independent sufficient conditions both on stochastic discounting processes for the habit formation process and on the utility function for the validity of several key assertions of our main results to hold true.
    Date: 2011–12
  13. By: Juan M. Londono
    Abstract: This paper investigates the variance risk premium in an international setting. First, I provide new evidence on the basic stylized facts traditionally documented for the US. I show that while the variance premiums in several other countries are, on average, positive and display significant time variation, they do not predict local equity returns. Then, I extend the domestic model in Bollerslev, Tauchen and Zhou (2009) to an international setting. In light of the qualitative implications of my model, I provide empirical evidence that the US variance premium outperforms that of all other countries in predicting local and foreign equity returns.
    Date: 2011

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