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on Utility Models and Prospect Theory |
| By: | Peter Klibanoff; Massimo Marinacci; Sujoy Mukerji |
| Abstract: | Epstein (2009) describes three Ellsberg-style thought experiments and argues that they pose difficulties for the smooth ambiguity model of decision making under uncertainty developed by Klibanoff, Marinacci and Mukerji (2005). We revisit these thought exeperiments and find, to the contrary, that they either point to strengths of the smooth ambiguity model compared to other models, such as the maximum expected utility model (Gilboa and Schmeidler, 1989), or, in the case of one thought experiment, raise criticisms that apply equally to a broad range of current ambiguity models. |
| Keywords: | Ambiguity, Uncertainty, Knightian uncertainty, Ambiguity aversion, Uncertainty aversion, Ellsberg paradox, Ambiguity attitude |
| JEL: | D80 D81 |
| Date: | 2009 |
| URL: | http://d.repec.org/n?u=RePEc:oxf:wpaper:449&r=upt |
| By: | Laetitia Andrieu (EDF R&D); Michel De Lara (CERMICS); Babacar Seck (CERMICS) |
| Abstract: | We provide an economic interpretation of the practice consisting in incorporating risk measures as constraints in a classic expected return maximization problem. For what we call the infimum of expectations class of risk measures, we show that if the decision maker (DM) maximizes the expectation of a random return under constraint that the risk measure is bounded above, he then behaves as a ``generalized expected utility maximizer'' in the following sense. The DM exhibits ambiguity with respect to a family of utility functions defined on a larger set of decisions than the original one; he adopts pessimism and performs first a minimization of expected utility over this family, then performs a maximization over a new decisions set. This economic behaviour is called ``Maxmin under risk'' and studied by Maccheroni (2002). This economic interpretation allows us to exhibit a loss aversion factor when the risk measure is the Conditional Value-at-Risk. |
| Date: | 2009–06 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:0906.3425&r=upt |
| By: | GIERLINGER, Johannes; GOLLIER, Christian |
| Date: | 2008–11 |
| URL: | http://d.repec.org/n?u=RePEc:ide:wpaper:9848&r=upt |
| By: | André Lapied (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - Université de la Méditerranée - Aix-Marseille II - Université Paul Cézanne - Aix-Marseille III - Ecole des Hautes Etudes en Sciences Sociales - CNRS : UMR6579); Pascal Toquebeuf (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - Université de la Méditerranée - Aix-Marseille II - Université Paul Cézanne - Aix-Marseille III - Ecole des Hautes Etudes en Sciences Sociales - CNRS : UMR6579) |
| Abstract: | This paper studies the application of the two most popular non-expected utility (NEU) models -Choquet Expected Utility (CEU) and Maximin Expected Utility (CEU)- to dynamic choice situations in a purely subjective framework. We give an appropriate version of the reduction of compound acts axiom, that states the equivalence between a static and a dynamic choice situation. We show that if consequentialism -only those consequences that can be reached do matter- is additionally assumed, then a monotonic constant linear representation degenerate into expected utility. We envisage two different ways to resolve this problem for the cases where the representation is a CEU or a MEU one. One way consists to weaken the reduction of compound acts axiom, which does not hold on all events. Another way is to relax consequentialism. Then we axiomatically characterize an updating rule for both approaches allowing recursion in several cases. |
| Keywords: | Choquet expected utility; Maximin expected utility; Consequentialism; Reduction of compound acts; Dynamic choice; Updating |
| Date: | 2009–09–13 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-00416214_v1&r=upt |
| By: | Hill, Brian |
| Abstract: | This paper proposes a model of the decision-maker’s confidence in his probability judgements, in terms of an implausibility measure – a real-valued function on the set of probability functions. A decision rule is axiomatised according to which the decision-maker evaluates acts using sets of probability functions which vary depending on the agent’s implausibility measure and on what is at stake in the choice of the act. The framework proposed yields a natural notion of comparative aversion to lack of confidence, or ambiguity aversion, and allows the definition of an ambiguity premium. It is shown that these notions are equivalent and can be characterised in terms of the implausibility measure representing the agent’s confidence. A simple portfolio example is presented. |
| Keywords: | Confidence; multiple priors; ambiguity aversion; ambiguity premium; implausibility measure |
| JEL: | C69 D81 |
| Date: | 2009–02–20 |
| URL: | http://d.repec.org/n?u=RePEc:ebg:heccah:0914&r=upt |
| By: | Kontek, Krzysztof |
| Abstract: | This paper discusses solutions derived from lottery experiments using two contradicting assumptions: that people perceive wealth changes as absolute amounts of money; and that people consider wealth changes as a proportion of some reference value dependant on the context of the problem under consideration. The former assumption leads to the design of Prospect Theory, the latter - to the aspiration / relative utility function (Kontek, 2009a), a solution closely resembling the utility function hypothesized by Markowitz (1952). This paper presents several crucial arguments for the latter approach, the major one being that people regard changes in wealth in a relative way is founded on Weber’s Law. This fundamental law of psychophysics contradicts the claim that gains and losses are perceived in absolute terms. Second, the absolute notion inevitably leads to the concept of probability weighting having to be incorporated into the descriptive model. This is not necessary when gains and losses are considered as relative values. Finally, the absolute notion leads to ambiguous solutions in that many different explanations for people’s behavior may be derived from the same set of experimental data. No such danger exists with the relative notion of gains and losses. This paper therefore provides strong arguments for rejecting the Prospect Theory approach and lays a foundation for a new Relative Utility Theory in the field of decision making under conditions of risk. |
| Keywords: | Prospect / Cumulative Prospect Theory; Probability Weighting Function; Markowitz Hypothesis; Aspiration / Relative Utility Function / Theory; Mental Accounts; Problem Framing and Scaling; Psychophysics; Weber’s Law; Experimental Design; Lottery; Decision Making Under Risk. |
| JEL: | D81 D01 D87 C91 |
| Date: | 2009–09–16 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:17336&r=upt |
| By: | Hayat Khan |
| Abstract: | Taking note of the wide variety and growing list of models in the literature to explain patterns of behavior observed in laboratory experiments, this paper identifies two tests, the Variety Test (ability of a model to explain outcomes under variety or alternative scenarios) and the Psychological Test (ability of a model to conform to psychological intuition), that can be used to judge any model of other-regarding behavior. It is argued that for a mathematical model to qualify as a social welfare function, it must simultaneously pass the two tests. It is shown that none of the models proposed to date passes these two tests simultaneously. The paper proposes a generalized model of inequity aversion which parsimoniously explains interior solution in the dictator game and dynamics of outcomes in other games. The paper postulates that one’s idea of equitable distribution is state-dependent, where the state is determined by psychological and structural parameters. The state could be fair, superior or inferior. Individuals in a fair state have zero equity-bias and split the pie evenly. Those in a superior (inferior) state have positive (negative) equity-bias and value more (less) than fair distribution as equitable distribution. Given psychological tendencies of an individual, every experimental design/structure assigns one of the three states to players which lead to individual-specific valuation of equity. Prediction about outcomes across different experiments and designs can be made through predicting their impact on equity-bias. All aspects of an individual’s behavior, such as altruism, fairness, reciprocity, self-serving bias, kindness, intentions etc, manifest themselves in the equity-bias. The model therefore is all-encompassing. |
| Keywords: | Experimental Economics, Social Preferences, Other-regarding Preferences, Inequity aversion. |
| JEL: | B4 C9 D8 O1 |
| Date: | 2009–09–21 |
| URL: | http://d.repec.org/n?u=RePEc:eei:rpaper:eeri_rp_2009_21&r=upt |
| By: | Alpizar, Francisco (Environment for Development Center, Tropical Agricultural and Higher Education Center (CATIE)); Carlsson, Fredrik (Department of Economics, School of Business, Economics and Law, Göteborg University); Naranjo, Maria (Environment for Development Center, Tropical Agricultural and Higher Education Center (CATIE)) |
| Abstract: | The risk of loses of income and productive means due to adverse weather associated to climate change can significantly differ between farmers sharing a productive landscape. It is important to learn more about how farmers react to different levels of risk, under measurable and unmeasurable uncertainty. Moreover, the costs associated to investments in reduced vulnerability to climatic events are likely to exhibit economies of scope. We explore these issues using a framed field experiment that captures realistically the main characteristics of production, and the likely weather related loses of premium coffee farmers in Tarrazu, Costa Rica. Given that the region recently was severely hit by an extreme, albeit very infrequent, climatic event, we expected to observe, and found high levels of risk aversion, but we do observe farmers making trade offs under different risk levels. Although hard to disentangle at first sight given the high level of risk aversion, we find that farmer’s opt more frequently for safe options in a setting characterized by unknown risk. Finally, we find that farmers to a large extent are able to coordinate their decisions in order to achieve a lower cost of adaptation, and that communication among farmers strongly facilitates coordination.<p> |
| Keywords: | Risk aversion; ambiguity aversion; technology adoption; climate change; field experiment |
| JEL: | C93 D81 H41 Q16 Q54 |
| Date: | 2009–09–21 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:gunwpe:0382&r=upt |
| By: | A. A. Brown |
| Abstract: | This note will extend the research presented in Brown & Rogers (2009) to the case of CRRA agents. We consider the model outlined in that paper in which agents had diverse beliefs about the dividends produced by a risky asset. We now assume that the agents all have CRRA utility, with some integer coefficient of relative risk aversion. This is a generalisation of Brown & Rogers which considered logarithmic agents. We derive expressions for the state price density, riskless rate, stock price and wealths of the agents. This sheds light on the effects of risk aversion in an equilibrium with diverse beliefs. |
| Date: | 2009–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:0907.4964&r=upt |
| By: | Michele Gori (Dipartimento di Matematica per le Decisioni, Universita' degli Studi di Firenze); Giulio Pianigiani (Dipartimento di Matematica per le Decisioni, Universita' degli Studi di Firenze) |
| Abstract: | In this paper we characterize metric spaces used in Beardon's generalization of Arrow-Hahn utility representation method as generalized Peano continua. For continuous preference relations defined on such metric spaces, we further construct an upper semi-continuous utility function which explicitly depends on the distance. |
| Keywords: | preference relation, utility function, convex metric space, generalized Peano continuum |
| JEL: | D11 |
| Date: | 2009–09 |
| URL: | http://d.repec.org/n?u=RePEc:flo:wpaper:2009-03&r=upt |
| By: | Michel De Lara (CERMICS) |
| Abstract: | Consider an agent taking two successive decisions to maximize his expected utility under uncertainty. After his first decision, a signal is revealed that provides information about the state of nature. The observation of the signal allows the decision-maker to revise his prior and the second decision is taken accordingly. Assuming that the first decision is a scalar representing consumption, the \emph{precautionary effect} holds when initial consumption is less in the prospect of future information than without (no signal). \citeauthor{Epstein1980:decision} in \citep*{Epstein1980:decision} has provided the most operative tool to exhibit the precautionary effect. Epstein's Theorem holds true when the difference of two convex functions is either convex or concave, which is not a straightforward property, and which is difficult to connect to the primitives of the economic model. Our main contribution consists in giving a geometric characterization of when the difference of two convex functions is convex, then in relating this to the primitive utility model. With this tool, we are able to study and unite a large body of the literature on the precautionary effect. |
| Date: | 2009–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:0907.4093&r=upt |
| By: | Chabi-Yo, Fousseni (Ohio State University) |
| Abstract: | I investigate a pricing kernel in which coskewness and the market volatility risk factors are endogenously determined. I show that the price of coskewness and market volatility risk are restricted by investor risk aversion and skewness preference. The risk aversion is estimated to be between two and five and significant. The price of volatility risk ranges from -1.5% to -0.15% per year. Consistent with theory, I find that the pricing kernel is decreasing in the aggregate wealth and increasing in the market volatility. When I project my estimated pricing kernel on a polynomial function of the market return, doing so produces the puzzling behaviors observed in pricing kernel. Using pricing kernels, I examine the sources of the idiosyncratic volatility premium. I find that nonzero risk aversion and firms' non-systematic coskewness determine the premium on idiosyncratic volatility risk. When I control for the non-systematic coskewness factor, I find no significant relation between idiosyncratic volatility and stock expected returns. My results are robust across different sample periods, different measures of market volatility and firm characteristics. |
| Date: | 2009–03 |
| URL: | http://d.repec.org/n?u=RePEc:ecl:ohidic:2008-25&r=upt |
| By: | Francesco Bogliacino; Giorgio Rampa |
| Abstract: | In this paper we provide a generalization of the standard models of the diffusion of a new product. Consumers are heterogeneous and risk averse, and the firm is uncertain about the demand curve: both learn from past observations. The attitude towards risk has important effects with regard to the diffusion pattern. In our model, downward-biased signals to consumers can prevent the success of the product, even if its objective quality is high: a “lock-in” result. We show in addition that the standard logistic pattern can be derived from the model. Finally, we discuss the asymptotic behavior of the learning dynamics, with regard to the multiplicity and the stability of equilibria, and to their welfare properties. |
| Keywords: | Heterogeneity, Multiple equilibria, Lock-in, Product diffusion, Risk aversion. |
| JEL: | L15 D81 O33 |
| Date: | 2009–09–27 |
| URL: | http://d.repec.org/n?u=RePEc:eei:rpaper:eeri_rp_2009_27&r=upt |
| By: | André De Palma (ENS Cachan - Ecole Normale Supérieure de Cachan - Ecole Normale Supérieure de Cachan, Department of Economics, Ecole Polytechnique - CNRS : UMR7176 - Polytechnique - X); Karim Kilani (CNAM - Conservatoire National des Arts et Métiers-Paris - CNAM) |
| Abstract: | We study the descriptive and the normative consequences of price and/or other attributes changes in additive random utility models. We first derive expressions for the transition choice probabilities associated to these changes. A closed-form formula is obtained for the logit. We then use these expressions to compute the cumulative distribution functions of the compensating variation conditional on ex-ante and/or ex-post choices. The unconditional distribution is also provided. The conditional moments of the compensating variation are obtained as a one-dimensional integral of the transition choice probabilities. This framework allows us to derive a stochastic version of Shephard's lemma, which relates the expected conditional compensating variation and the transition choice probabilities. We compute the compensating variation for a simple binary linear in income choice model and show that the information on the transitions leads to better estimates of the compensating variation than those obtained when only ex-ante or ex-post information on individual choices is observed. For the additive in income logit, we compute the conditional distribution of compensating variation, which generalizes the logsum formula. Finally, we derive a new welfare formula for the disaggregated version of the represen- tative consumer CES model. |
| Keywords: | Additive random utility models (ARUM), Logit, Transition choice probabilities, Compensating variation, Shephard's Lemma, Logsum, CES |
| Date: | 2009–09–16 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-00417493_v1&r=upt |
| By: | Constant Tra (Department of Economics, University of Nevada, Las Vegas) |
| Abstract: | The paper investigates the implications of nonlinear income effects in random utility models (RUM) for measuring non-marginal welfare impacts. A popular approach in applied welfare analysis is to approximate the expected compensating variation (cv) for an amenity change as the cv of a representative consumer whose indirect utility is given by the expected maximum utility. However, this approach can be misleading in the case of non-marginal changes as it implies that changes in income do not affect the consumer’s choice. In this case the true expected cv can be obtained via simulation. Empirical applications to recreational demand find that the bias from the representative approach is small. This paper re-evaluates the accuracy of the representative consumer approximation in the context of measuring the general equilibrium welfare impacts of large environmental changes. Our findings suggest that, though the representative consumer approximation could lead to biased point estimates of the expected cv, this bias is overwhelmed by the size of the confidence intervals that result from the empirical estimation of household preferences. |
| Keywords: | compensating variation, nonlinear income effects, discrete choice |
| JEL: | Q51 R21 |
| Date: | 2009–03 |
| URL: | http://d.repec.org/n?u=RePEc:nlv:wpaper:0924&r=upt |
| By: | Jaume Masoliver; Josep Perello |
| Abstract: | We solve the first-passage problem for the Heston random diffusion model. We obtain exact analytical expressions for the survival and hitting probabilities to a given level of return. We study several asymptotic behaviors and obtain approximate forms of these probabilities which prove, among other interesting properties, the non-existence of a mean first-passage time. One significant result is the evidence of extreme deviations --which implies a high risk of default-- when certain dimensionless parameter, related to the strength of the volatility fluctuations, increases. We believe that this may provide an effective tool for risk control which can be readily applicable to real markets. |
| Date: | 2009–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:0902.2735&r=upt |
| By: | Itzhak Gilboa |
| Date: | 2009–09–06 |
| URL: | http://d.repec.org/n?u=RePEc:cla:levarc:814577000000000335&r=upt |
| By: | Peter Klibano; Massimo Marinacci; Sujoy Mukerji |
| Date: | 2009–09–10 |
| URL: | http://d.repec.org/n?u=RePEc:cla:levarc:814577000000000344&r=upt |
| By: | Eddie Dekel; Barton L. Lipman |
| Date: | 2009–09–06 |
| URL: | http://d.repec.org/n?u=RePEc:cla:levarc:814577000000000339&r=upt |
| By: | Jose E. Figueroa-Lopez; Jin Ma |
| Abstract: | We revisit Merton's portfolio optimization problem under boun-ded state-dependent utility functions, in a market driven by a L\'evy process $Z$ extending results by Karatzas et. al. (1991) and Kunita (2003). The problem is solved using a dual variational problem as it is customarily done for non-Markovian models. One of the main features here is that the domain of the dual problem enjoys an explicit "parametrization", built on a multiplicative optional decomposition for nonnegative supermartingales due to F\"ollmer and Kramkov (1997). As a key step in obtaining the representation result we prove a closure property for integrals with respect to Poisson random measures, a result of interest on its own that extends the analog property for integrals with respect to a fixed semimartingale due to M\'emin (1980). In the case that (i) the L\'evy measure of $Z$ is atomic with a finite number of atoms or that (ii) $\Delta S_{t}/S_{t^{-}}=\zeta_{t} \vartheta(\Delta Z_{t})$ for a process $\zeta$ and a deterministic function $\vartheta$, we explicitly characterize the admissible trading strategies and show that the dual solution is a risk-neutral local martingale. |
| Date: | 2009–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:0901.2070&r=upt |
| By: | Xuehong Wang (Centre for Environmental Management, Central Queensland University, Australia); John Rolfe (Regional Development Economics, Faculty of Business and Informatics, Central Queensland University, Australia) |
| Abstract: | Many policy issues, as well as policy funding and management choices, have elements of risk and uncertainty. This means that choice experiments, such as those used in choice modelling (CM), may need to frame trade-offs so that risk and uncertainty are included.This research aims to explore some methodological approaches to identify and treat uncertainty in CM experiments. A review of theoretical models, as well as a case study application in the CM technique reported by Roberts et al. (2008), suggests that including uncertainty information in the choice sets should influence responses significantly. However, key challenges remain to define and describe the elements of risk and uncertainty that are to be included in a choice experiment, to communicate the issues to respondents, and to develop appropriate forms of analysis. |
| Date: | 2009–01 |
| URL: | http://d.repec.org/n?u=RePEc:een:eenhrr:0912&r=upt |
| By: | Finkelstein, Amy N. (MIT); Luttmer, Erzo F. P. (Harvard University and IZA, Bonn); Notowidigdo, Matthew J. (MIT) |
| Abstract: | If the marginal utility of consumption depends on health status, this will affect the economic analysis of a number of central problems in public finance, including the optimal structure of health insurance and optimal life cycle savings. In this paper, we describe the promises and challenges of various approaches to estimating the effect of health on the marginal utility of consumption. Our basic conclusion is that while none of these approaches is a panacea, many offer the potential to shed important insights on the nature of health state dependence. |
| JEL: | D12 I10 |
| Date: | 2009–01 |
| URL: | http://d.repec.org/n?u=RePEc:ecl:harjfk:rwp09-002&r=upt |
| By: | Adam Clements (QUT); Annastiina Silvennoinen (QUT) |
| Abstract: | Forecasts of asset return volatility are necessary for many financial applications, including portfolio allocation. Traditionally, the parameters of econometric models used to generate volatility forecasts are estimated in a statistical setting and subsequently used in an economic setting such as portfolio allocation. Differences in the criteria under which the model is estimated and applied may inhibit reduce the overall economic benefit of a model in the context of portfolio allocation. This paper investigates the economic benefit of direct utility based estimation of the parameters of a volatility model and allows for practical issues such as transactions costs to be incorporated within the estimation scheme. In doing so, we compare the benefits stemming from various estimators of historical volatility in the context of portfolio allocation. It is found that maximal utility based estimation, taking into account transactions costs, of a simple volatility model is preferred on the basis of greater realized utility. Estimation of models using historical daily returns is preferred over historical realized volatility. |
| Keywords: | Volatility, utility, portfolio allocation, realized volatility, MIDAS |
| JEL: | C10 C22 G11 |
| Date: | 2009–07–21 |
| URL: | http://d.repec.org/n?u=RePEc:qut:auncer:2009_57&r=upt |