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on Utility Models and Prospect Theory |
| By: | Karle, Heiko; Kirchsteiger, Georg; Peitz, Martin |
| Abstract: | In this paper we analyze a consumer choice model with price uncertainty, loss aversion, and expectation-based reference points. The implications of this model are tested in an experiment in which participants have to make a consumption choice between two sandwiches. We make use of the fact that participants differ in their reported taste difference between the two sandwiches and the degree of loss aversion which we measure separately. We find that more loss-averse participants are more likely to opt for the cheaper sandwich provided that their reported taste difference is below some threshold, confirming the model’s predictions. |
| Keywords: | Contextual Reference Points; Loss Aversion; Reference-Dependent Utility |
| JEL: | C91 D01 D11 D83 |
| Date: | 2012–10 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:9183&r=upt |
| By: | Matteo Del Vigna (Dipartimento di Matematica per le Decisioni - Universita' degli Studi di Firenze) |
| Abstract: | We study the connections between stochastic dominance and law invariant preferences. Whenever the functional that represents preferences depends only on the law of the random variable, we shall look for conditions that imply a ranking of distributions. In analogy with the Expected Utility paradigm, we prove that functional dominance leads to first order stochastic dominance. We analyze in details the case of Dual Theory of Choice and Cumulative Prospect Theory, including all its distinctive features such as S-shaped value function, reversed S-shaped probability distortions and loss aversion. These cases can be seen as special examples of a more general scheme. We find necessary and sufficient conditions that imply preferences to depend only on the mean and variance of the lottery. Our main result is a characterization of such distributions that imply Mean-Variance preferences, namely the elliptical ones. In particular, we prove that under mild assumptions over the reference wealth, the prospect value of a portfolio depends only on its mean and variance if and only if the random assets' return are elliptically distributed. The analysis is of particular relevance for optimal portfolio choice, mutual fund separation and Capital Asset Pricing equilibria. |
| Keywords: | Stochastic dominance, Cumulative Prospect Theory, Elliptical distributions, Mean-Variance analysis. |
| JEL: | D03 D81 G11 |
| Date: | 2012–10 |
| URL: | http://d.repec.org/n?u=RePEc:flo:wpaper:2012-08&r=upt |
| By: | Paola Manzini; Marco Mariotti |
| Abstract: | We model a boundedly rational agent who suffers from limited attention. The agent considers each feasible alternative with a given (unobservable) probability, the attention parameter, and then chooses the alternative that maximises a preference relation within the set of considered alternatives. Both the preference and the attention parameters are identified uniquely by stochastic choice data. The model is the only one for which the impact of removing any alternative a on the choice probability of any other alternative b is non-negative, asymmetric (either a impacts b or vice-versa), menu independent, neutral (the same on any alternative in the menu), and consistent with the impacts on a and b by a common third alternative. |
| Keywords: | Discrete choice, Random utility, Logit model, Consideration sets, bounded rationality, revealed preferences |
| JEL: | D0 |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:trn:utwpce:1205&r=upt |
| By: | Mario Ghossoub |
| Abstract: | I examine a class of utility maximization problems with a not necessarily law-invariant utility, and with a not necessarily law-invariant risk measure constraint. The objective function is an integral of some function U with respect to some probability measure P, and the constraint set contains some risk measure constraint which is not necessarily P-law-invariant. This introduces some heterogeneity in the perception of uncertainty. The primitive U is a function of some given underlying random variable X and of a contingent claim Y on X. Many problems in economic theory and financial theory can be formulated in this manner, when a heterogeneity in the perception of uncertainty is introduced. Under a consistency requirement on the risk measure that will be called Vigilance, supermodularity of the primitive U is sufficient for the existence of optimal continent claims, and for these optimal claims to be comonotonic with the underlying random variable X. Vigilance is satisfied by a large class of risk measures, including all distortion risk measures. An explicit characterization of an optimal contingent claim is also provided in the case where the risk measure is a convex distortion risk measure. |
| Keywords: | Contingent Claims, Heterogeneous Beliefs, Choquet Integral, Vigilance, Monotone Likelihood Ratio JEL Classification Numbers: C02, D81, D89, G11 |
| Date: | 2012–10–22 |
| URL: | http://d.repec.org/n?u=RePEc:nwu:cmsems:1555&r=upt |
| By: | Bianca De Paoli; Pawel Zabczyk |
| Abstract: | This paper studies the policy implications of habits and cyclical changes in agents' appetite for risk-taking. To do so, it analyses the non-linear solution of a New Keynesian (NK) model, in which slow-moving habits help match the cyclical properties of risk-premia. Our findings suggest that the presence of habits and swings in risk appetite can materially affect policy prescriptions. As in Ljungqvist and Uhlig (2000), a counter-cyclical fiscal instrument can eliminate habit-related externalities. Alternatively, monetary policy can partially curb the associated overconsumption by responding to risk premia. Specifically, periods in which risk premia are elevated (compressed) merit a looser (tighter) policy stance. However, the associated welfare gains appear quantitatively small. |
| Keywords: | Policy design, cyclical risk aversion, New Keynesian model, habit formation |
| JEL: | E32 G12 |
| Date: | 2012–10 |
| URL: | http://d.repec.org/n?u=RePEc:cep:cepdps:dp1170&r=upt |
| By: | Martín Egozcue (Universidad de la República); Sébastien Massoni (Centre d'Economie de la Sorbonne - Paris School of Economics); Wing-Keung Wong (Hong Kong Baptist University); Ri?ardas Zitikis (University of Western Ontario) |
| Abstract: | Whether to keep products segregated (e.g., unbundled) or integrate some or all of them (e.g., bundle) has been a problem of profound interest in areas such as portfolio theory in finance, risk capital allocations in insurance, and marketing of consumer products. Such decisions are inherently complex and depend on factors such as the underlying product values and consumer preferences, the latter being frequently described using value functions, also known as utility functions in economics. In this paper, we develop decision rules for multiple products, which we generally call ‘exposure units’ to naturally cover manifold scenarios spanning well beyond ‘products’. Our findings show, for example, that the celebrated Thaler's principles of mental accounting hold as originally postulated when the values of all exposure units are positive (i.e., all are gains) or all negative (i.e., all are losses). In the case of exposure units mixed-sign values, decision rules are much more complex and rely on cataloging the Bell-number of cases that grow very fast depending on the number of exposure units. Consequently, in the present paper we provide detailed rules for the integration and segregation decisions in the case up to three exposure units, and partial rules for the arbitrary number of units. |
| Keywords: | Bundling, marketing, mental accounting, portfolio theory, value function, utility function, majorization, functional inequalities, Bell number. |
| JEL: | C61 D01 D81 M31 |
| Date: | 2012–09 |
| URL: | http://d.repec.org/n?u=RePEc:mse:cesdoc:12057&r=upt |
| By: | Hjorth, Katrine; Fosgerau, Mogens |
| Abstract: | A common finding in stated preference studies that measure the value of travel time (VTT) is that the measured VTT increases with the size of the time change considered, in conflict with standard neoclassical economic theory. We present a new test of a possible explanation for the phenomenon that builds on the diminishing or constant sensitivity of the value functions in prospect theory. We use stated preference data with trade-offs between travel time and money that provide separate identification of the degrees of diminishing sensitivity for time and money gains and losses. This enables us to test and potentially falsify the prospect theory explanation. We conclude that prospect theory remains a potential explanation of the phenomenon. |
| Keywords: | Value of travel time; Stated preference data; Prospect theory; Small time savings |
| JEL: | D12 C35 R41 |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:42246&r=upt |
| By: | Rodríguez, Alejandro; Ruiz, Esther |
| Abstract: | In the context of linear state space models with known parameters, the Kalman filter (KF) generates best linear unbiased predictions of the underlying states together with their corresponding Prediction Mean Square Errors (PMSE). However, in practice, when the filter is run with the parameters substituted by consistent estimates, the corresponding PMSE do not take into account the parameter uncertainty. Consequently, they underestimate their true counterparts. In this paper, we propose two new bootstrap procedures to obtain PMSE of the unobserved states designed to incorporate this latter uncertainty. We show that the new bootstrap procedures have better finite sample properties than bootstrap alternatives and than procedures based on the asymptotic approximation of the parameter distribution. The proposed procedures are implemented for estimating the PMSE of several key unobservable US macroeconomic variables as the output gap, the Non-accelerating Inflation Rate of Unemployment (NAIRU), the long-run investment rate and the core inflation. We show that taking into account the parameter uncertainty may change their prediction intervals and, consequently, the conclusions about the utility of the NAIRU as a macroeconomic indicator for expansions and recessions. |
| Keywords: | NAIRU; Output gap; Parameter uncertainty; Prediction intervals; State space models; |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:ner:carlos:info:hdl:10016/15743&r=upt |
| By: | Zhi Zheng; Richard B. Sowers |
| Abstract: | In this paper we introduce a completely continuous and time-variate model of the evolution of market limit orders based on the existence, uniqueness, and regularity of the solutions to a type of stochastic partial differential equations obtained in Zheng and Sowers (2012). In contrary to several models proposed and researched in literature, this model provides complete continuity in both time and price inherited from the stochastic PDE, and thus is particularly suitable for the cases where transactions happen in an extremely fast pace, such as those delivered by high frequency traders (HFT's). We first elaborate the precise definition of the model with its associated parameters, and show its existence and uniqueness from the related mathematical results given a fixed set of parameters. Then we statistically derive parameter estimation schemes of the model using maximum likelihood and least mean-square-errors estimation methods under certain criteria such as AIC to accommodate to variant number of parameters . Finally as a typical economics and finance use case of the model we settle the investment optimization problem in both static and dynamic sense by analysing the stochastic (It\^{o}) evolution of the utility function of an investor or trader who takes the model and its parameters as exogenous. Two theorems are proved which provide criteria for determining the best (limit) price and time point to make the transaction. |
| Date: | 2012–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1210.7230&r=upt |
| By: | SHIMIZUTANI Satoshi; OSHIO Takashi |
| Abstract: | This paper explores the public pension claiming behavior of the Japanese. First, we perform financial simulations and estimate the expected utility, depicting the typical patterns of pension benefits in a lifecycle model. We show that the optimal retirement age depends on the beneficiaries' mortality risk, discount rate, initial wealth, and risk attitude. Second, we use individual-level data from the Japanese Study on Aging and Retirement to examine empirically the determinants of the take-up timing. We find supportive evidence that most of the factors examined in the simulation are indeed significantly associated with early claiming of pension benefits for wage earners. |
| Date: | 2012–10 |
| URL: | http://d.repec.org/n?u=RePEc:eti:dpaper:12068&r=upt |
| By: | Allen, D.; Lizieri, C.; Satchell, S. |
| Abstract: | Mean-variance optimisation has been roundly criticised by financial economists and practitioners alike, leading many to advocate a simple 1/N weighting heuristic. We investigate the performance of the Markowitz technique conditional on investor forecasting ability. Using a novel analytical approach, we demonstrate that investors with a modicum of forecasting ability can employ mean-variance to significantly increase their ex ante utility, outperforming the 1/N rule. |
| Keywords: | Portfolio Choice; Investment Decisions; Financial Forecasting and Simulation |
| JEL: | G11 G17 |
| Date: | 2012–10–19 |
| URL: | http://d.repec.org/n?u=RePEc:cam:camdae:1244&r=upt |