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on Utility Models and Prospect Theory |
| By: | Ian Jewitt; Sujoy Mukerji |
| Abstract: | We investigate what it means for one actot be more ambiguous than another. The question is evidently analogous to asking what makes one prospect rikier than another, but beliefs are neither objective nor representatable by a unique probability. Our starting point is an abstract class of preferences constructed to be (strictly) partially ordered by a more ambiguity averse relation. We define two notions of more ambiguous with respect to such a class. A more ambiguous (I) act makes an ambiguity averse decision maker (DM) worse off but does not affect the welfare of an ambiguity neutral DM. A more ambiguous (II) act adversely affects a more ambiguity averse DM more, as measured by the compensation they require to switch acts. Unlike more ambiguous (I), more ambiguous (II) does not require indiffrence of ambiguity neutral elements to the acts being compared. SEcond, we implement the abstract definitions to characterize more ambiguous (I) and (II) for two explicit preference families: a-maxmin expected utility and smooth ambiguity. Our characterization show that (the outcome of) a more ambiguous act is less robust to a perturbation in probability distribution governing the states. Third, the characterizations also establish important connections between more ambiguous and more informative as defined on statistical experiments by Blackwell (1953) and others. Fourthly, we give applications to defining ambiguity "in the small" and to the comparative statics of more ambiguous in a standard portfolio problem and a consmption-saving problem. |
| Keywords: | Ambiguity, Uncertainty, Knightian uncertainty, Ambiguity aversion, Uncertainty aversion, Ellsberg paradox, Comparative statistics, Single-crossing, More ambiguous, Portfolio choice, More informative, Information, Garbling. |
| JEL: | C44 D80 D81 G11 |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:oxf:wpaper:553&r=upt |
| By: | Brahim Brahimi; Djamel Meraghni; Abdelhakim Necir |
| Abstract: | We discuss two distinct approaches, for distorting risk measures of sums of dependent random variables, which preserve the property of coherence. The first, based on distorted expectations, operates on the survival function of the sum. The second, simultaneously applies the distortion on the survival function of the sum and the dependence structure of risks, represented by copulas. Our goal is to propose risk measures that take into account the fluctuations of losses and possible correlations between risk components. |
| Date: | 2011–06 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1106.2791&r=upt |
| By: | Jose-Luis Pinto-Prades (Department of Economics, Universidad Pablo de Olavide); Jose-Maria Abellan-Perpiñan (Department of Applied Economics, Universidad de Murcia) |
| Abstract: | Revealed preferences are not consistent. Many anomalies have been found in different contexts. This finding leads to a divergence between normative and descriptive analyses. There are several ways of facing this problem. In this paper we argue in favour of debiasing observed choices in such a way that the “true” preferences are discovered. Our procedure is based on quantitative corrections derived from assuming the descriptive validity of prospect theory and the normative validity of Expected Utility. Those corrective formulas were first applied by Bleichrodt et al. (2001). We explain here how such formulas can be used to avoid inefficient allocation of health care resources. This approach shares the philosophy of Libertarian Paternalism (LP). However, it reduces some of the potential problems of LP: the definition of error (and the need to nudge people) is more clear and objective. In this sense, it reduces the chances that the regulator tries to nudge people toward behaviour based on her preferences and not on subject’s own preferences. |
| Keywords: | Social debiasing, true preferences, prospect theory, discovered preferences hypothesis, libertarian paternalism. |
| JEL: | I10 |
| Date: | 2011–06 |
| URL: | http://d.repec.org/n?u=RePEc:pab:wpaper:11.06&r=upt |
| By: | Xu, Yongsheng; Yoshihara, Naoki |
| Abstract: | Conditions α and β are two well-known rationality conditions in the theory of rational choice. This paper examines the implications of weaker versions of these two rationality conditions in the context of solutions to nonconvex bargaining problems. It is shown that, together with the standard axioms of efficiency and strict individual rationality, they imply rationalizability of solutions to nonconvex bargaining problems. We then characterize asymmetric Nash solutions by imposing a continuity and the scale invariance requirements. We also give a characterization of the Nash solution by using the two rationality conditions. These results make a further connection between solutions to non-convex bargaining problems and rationalizability of choice function in the theory of rational choice. |
| JEL: | C71 C78 D63 D71 |
| Date: | 2011–05 |
| URL: | http://d.repec.org/n?u=RePEc:hit:hituec:551&r=upt |
| By: | Xiaohong Chen; Jack Favilukis; Sydney C. Ludvigson |
| Abstract: | This paper presents estimates of key preference parameters of the Epstein and Zin (1989, 1991) and Weil (1989) (EZW) recursive utility model, evaluates the model's ability to fit asset return data relative to other asset pricing models, and investigates the implications of such estimates for the unobservable aggregate wealth return. Our empirical results indicate that the estimated relative risk aversion parameter ranges from 17-60, with higher values for aggregate consumption than for stockholder consumption, while the estimated elasticity of intertemporal substitution is above one. In addition, the estimated model-implied aggregate wealth return is found to be weakly correlated with the CRSP value-weighted stock market return, suggesting that the return to human wealth is negatively correlated with the aggregate stock market return. |
| JEL: | E21 G12 |
| Date: | 2011–06 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:17130&r=upt |
| By: | Belén Nieto (Departamento de Economía financiera y Contabilidad, Universidad de Alicante); Alfonso Novales Cinca (Departamento de Economía Cuantitativa (Department of Quantitative Economics), Facultad de Ciencias Económicas y Empresariales (Faculty of Economics and Business), Universidad Complutense de Madrid); Gonzalo Rubio (Universidad CEU Cardenal Herrera) |
| Abstract: | This paper studies the determinants of the variance risk premium and concludes on the hedging possibilities offered by variance swaps. We start by showing that the variance risk premium responds to changes in higher order moments of the distribution of market returns. But the uncertainty that determines the variance risk premium –the fear by investors to deviations from Normality in returns- is also strongly related to a variety of risks: risk of default, employment growth risk, consumption growth risk, stock market risk and market illiquidity risk. Therefore, the variance risk premium could be interpreted as reflecting the market willingness to pay for hedging against financial and macroeconomic sources of risk. We provide additional evidence in support of that view. |
| Keywords: | Variance risk premium, Non-normality, Economic risks, Hedging |
| JEL: | C13 C14 G10 G12 |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:ucm:doicae:1106&r=upt |
| By: | Ben-Tal, A; Hertog, D. den; De Waegenaere, A.M.B.; Melenberg, B.; Rennen, G. (Tilburg University, Center for Economic Research) |
| Abstract: | In this paper we focus on robust linear optimization problems with uncertainty regions defined by ø-divergences (for example, chi-squared, Hellinger, Kullback-Leibler). We show how uncertainty regions based on ø-divergences arise in a natural way as confidence sets if the uncertain parameters contain elements of a probability vector. Such problems frequently occur in, for example, optimization problems in inventory control or finance that involve terms containing moments of random variables, expected utility, etc. We show that the robust counterpart of a linear optimization problem with ø-divergence uncertainty is tractable for most of the choices of ø typically considered in the literature. We extend the results to problems that are nonlinear in the optimization variables. Several applications, including an asset pricing example and a numerical multi-item newsvendor example, illustrate the relevance of the proposed approach. |
| Keywords: | robust optimization;ø-divergence;goodness-of-fit statistics. |
| JEL: | C61 |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:kubcen:2011061&r=upt |