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on Utility Models and Prospect Theory |
| By: | Matteo Del Vigna (Dipartimento di Statistica e Matematica Applicata all'Economia, Universita' di Pisa & CEREMADE, Universite' Paris-Dauphine) |
| Abstract: | In this paper we review some well-known simple models for portfolio selection under Knightian uncertainty, also known as ambiguity, and we compute a number of explicit optimal portfolio rules using elementary mathematical tools. In the case of a single period financial market, new results arise for an agent who is risk neutral and smoothly ambiguity averse, for a loss averse and smoothly ambiguity averse agent, for a Mean-Variance and alpha-Maxmin Expected Utility agent. In a continuous time setting, we are able to recover some existing results on optimal investment strategies employing trivial stochastic analysis and avoiding the complicated BSDE machinery. |
| Keywords: | Knightian uncertainty, Maxmin Expected Utility, smooth ambiguity aversion, loss aversion |
| JEL: | D81 G11 |
| Date: | 2011–04 |
| URL: | http://d.repec.org/n?u=RePEc:flo:wpaper:2011-07&r=upt |
| By: | Noemi Pace (Department of Economics, University Of Venice Cà Foscari); John D Hey (Department of Economics, University of York) |
| Abstract: | Representing ambiguity in the laboratory using a Bingo Blower (which is transparent and not manipulable) and asking the subjects a series of allocation questions (which are more efficient than pairwise choice questions), we obtain data from which we can estimate by maximum likelihood methods (with explicit assumptions about the errors made by the subjects) a significant subset of the empirically relevant models of behaviour under ambiguity, and compare their relative explanatory and predictive abilities. Our results suggest that not all recent models of behaviour represent a major improvement in explanatory and predictive power, particularly the more theoretically sophisticated ones. |
| Keywords: | Alpha Model, Ambiguity, Bingo Blower, Choquet Expected Utility, Contraction Model, Rank Dependent Expected Utility, Subjective Expected Utility,Vector Expected Utility. |
| JEL: | D81 C9 |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:ven:wpaper:2011_12&r=upt |
| By: | Pavlo R. Blavatskyy |
| Abstract: | Empirical research often requires a method how to convert a deterministic economic theory into an econometric model. A popular method is to add a random error term on the utility scale. This method, however, violates stochastic dominance. A modification of this method is proposed to avoid violations of dominance. The modified model compares favorably to other existing models in terms of goodness of fit to experimental data. The modified model can rationalize the preference reversal phenomenon. An intuitive axiomatic characterization of the modified model is provided. Important microeconomic concept of risk aversion is well-defined in the modified model. |
| Keywords: | Decision Theory, Probabilistic Choice, Stochastic Dominance, Strong Utility, Risk Aversion |
| JEL: | C25 D81 |
| Date: | 2011–09 |
| URL: | http://d.repec.org/n?u=RePEc:inn:wpaper:2011-16&r=upt |
| By: | Alexander Zimper |
| Abstract: | In standard models of Bayesian learning agents reduce their uncertainty about an eventÂ’s true probability because their consistent estimator concentrates almost surely around this probabilityÂ’s true value as the number of observations becomes large. This paper takes the empirically observed violations of SavageÂ’s (1954) sure thing principle seriously and asks whether Bayesian learners with ambiguity attitudes will reduce their ambiguity when sample information becomes large. To address this question, I develop closed-form models of Bayesian learning in which beliefs are described as Choquet estimators with respect to neo-additive capacities (Chateauneuf, Eichberger, and Grant 2007). Under the optimistic, the pessimistic, and the full Bayesian update rule, a Bayesian learnerÂ’s ambiguity will increase rather than decrease to the effect that these agents will express ambiguity attitudes regardless of whether they have access to large sample information or not. While consistent Bayesian learning occurs under the Sarin-Wakker update rule, this result comes with the descriptive drawback that it does not apply to agents who still express ambiguity attitudes after one round of updating. |
| Keywords: | Non-additive Probability Measures, Bayesian Learning, Choquet Expected Utility Theory |
| JEL: | C11 D81 D83 |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:rza:wpaper:240&r=upt |
| By: | Matteo Del Vigna (Dipartimento di Statistica e Matematica Applicata all'Economia, Universita' di Pisa & CEREMADE , Universite' Paris-Dauphine) |
| Abstract: | Starting from the theory of portfolio selection under Cumulative Prospect Theory (CPT) in a one period model, we firstly present some remarks connected with the violation of the so-called loss aversion in the case of power utility functions. The main contribution of this paper comes from the analysis of two equilibrium models. In the first one, an Expected Utility (EU) maximizer, a CPT agent and an accommodating market maker are allowed to interact. We show that there can be equilibria with null, positive or total risky investment by the CPT trader. Our results are then compared to an analogous model with two EU maximizers. On the contrary, the second financial market is populated by a sufficiently large number of EU agents and CPT agents, each of them being price maker and endowed with possibly heterogeneous preferences, these two facts being new to the literature. This time EU traders fully invest in stocks whereas CPT traders stay out of the risky market. For both models, equilibrium existence and robustness is shown using analytical and numerical methods. |
| Keywords: | Cumulative Prospect Theory, equilibrium models, loss aversion, heterogeneous preferences, portfolio optimisation, volatility impact |
| JEL: | C62 D53 D81 G11 |
| Date: | 2011–04 |
| URL: | http://d.repec.org/n?u=RePEc:flo:wpaper:2011-09&r=upt |
| By: | Brice Mayag (LGI - Laboratoire Génie Industriel - EA 2606 - Ecole Centrale Paris); Michel Grabisch (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I); Christophe Labreuche (UMP CNRS/THALES - Unité mixte de physique CNRS/Thalès - CNRS : UMR137 - THALES) |
| Abstract: | In the context of Multiple criteria decision analysis, we present the necessary and sufficient conditions allowing to represent an ordinal preferential information provided by the decision maker by a Choquet integral w.r.t a 2-additive capacity. We provide also a characterization of this type of preferential information by a belief function which can be viewed as a capacity. These characterizations are based on three axioms, namely strict cycle-free preferences and some monotonicity conditions called MOPI and 2-MOPI. |
| Keywords: | multicriteria decision making; Choquet integral; 2-additive capacity; MACBETH |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:hal:cesptp:halshs-00625706&r=upt |
| By: | Patrick MOYES ( GREThA, CNRS, UMRS 5113); Nicolas GRAVEL (AMSE (GREQAM) et Aix-Marseille University) |
| Abstract: | We show that it is possible to reconcile the utilitarian and welfarist principles under the\r\nrequirement of unanimity provided that the set of profiles over which the consensus is\r\nattained is rich enough. More precisely, we identify a closedness condition which, if satisfied\r\nby a class of n-tuples of utility functions, guarantees that the rankings of social states\r\ninduced by utilitarian and welfarist unanimities over that class are identical. We illustrate the\r\nimportance of the result for the measurement of unidimensional as well as multidimensional\r\ninequalities from a dominance point of view |
| Keywords: | Unanimity, Utilitarianism, Welfarism, Stochastic Dominance |
| JEL: | D31 D63 I32 |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:grt:wpegrt:2011-30&r=upt |
| By: | Taisei Kaizoji; A. Saichev; D. Sornette |
| Abstract: | We introduce a model of financial bubbles with two assets (risky and risk-less), in which rational investors and noise traders co-exist. Rational investors form continuously evolving expectations on the return and risk of a risky asset and maximize their expected utility with respect to their allocation on the risky asset versus the risk-free asset. Noise traders are subjected to social imitation and follow momentum trading. We find the existence of a set of bifurcations controlled by the relative influence of noise traders with respect to rational investors that separate a normal regime of the price dynamics to a phase punctuated by recurrent exponentially explosive bubbles. The transition to a bubble regime is favored by noise traders who are more social, and who use more momentum trading with shorter time horizons. The model accounts well for the behavior of traders and for the price dynamics that developed during the dotcom bubble in 1995-2000. Momentum strategies are shown to be transiently profitable, supporting these strategies as enhancing herding behavior. |
| Date: | 2011–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1109.4726&r=upt |
| By: | Chaohua Dong; Jiti Gao |
| Abstract: | Two types of Brownian motion functionals, both time-homogeneous and time-inhomogeneous, are expanded in terms of orthonormal bases in respective Hilbert spaces. Meanwhile, different time horizons are treated from the applicability point of view. Moreover, the degrees of approximation of truncation series to the corresponding series are established. An asymptotic theory is established. Both the proposed expansions and asymptotic theory are applied to establish consistent estimators in a class of time series econometric models. |
| Keywords: | Asymptotic theory; Brownian motion; econometric estimation, series expansion. |
| JEL: | C14 C32 |
| Date: | 2011–09 |
| URL: | http://d.repec.org/n?u=RePEc:msh:ebswps:2011-19&r=upt |
| By: | Oechssler, Jörg |
| Abstract: | A well—known result from the theory of finitely repeated games states that if the stage game has a unique equilibrium, then there is a unique subgame perfect equilibrium in the finitely repeated game in which the equilibrium of the stage game is being played in every period. Here I show that this result does in general not hold anymore if players have social preferences of the form frequently assumed in the recent literature, for example in the inequity aversion models of Fehr and Schmidt (1999) or Bolton and Ockenfels (2000). In fact, repeating the unique stage game equilibrium may not be a subgame perfect equilibrium at all. |
| Keywords: | social preferences; finitely repeated games; inequity aversion; ERC |
| Date: | 2011–09–22 |
| URL: | http://d.repec.org/n?u=RePEc:awi:wpaper:0515&r=upt |