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on Utility Models and Prospect Theory |
| By: | Georges Dionne; Jingyuan Li |
| Abstract: | This paper studies comparative risk aversion between risk averse agents in the presence of a background risk. Although the literature covers this question extensively, our contribution differs from most of the literature in two respects. First, background risk does not need to be additive or multiplicative. Second, the two risks are not necessary mean independent, and may be quadrant dependent. We show that our order of cross Ross risk aversion is equivalent to that of partial risk premium, while our index of decreasing cross Ross risk aversion is equivalent to that of a decreasing partial risk premium. These results generalize the comparative risk aversion model developed by Ross (1981) for mean independent risks. Finally, we show that decreasing cross Ross risk aversion gives rise to the utility function family belonging to the class of n-switch utility functions. |
| Keywords: | Comparative cross Ross risk aversion, Quadrant dependent background risk, Partial risk premium, Decreasing cross Ross risk aversion, n-switch utility functions |
| JEL: | D81 |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:lvl:lacicr:1226&r=upt |
| By: | Kellner, Christian; Riener, Gerhard |
| Abstract: | We test the implications of ambiguity aversion in a principal-agent problem with multiple agents. Models of ambiguity aversion suggest that, under ambiguity, comparative compensation schemes may become more attractive than independent wage contracts. We test this by presenting agents with a choice between comparative reward schemes and independent contracts, which are designed such that under uncertainty about output distributions (that is, under ambiguity), ambiguity averse agents (and only those) should typically prefer comparative reward schemes, independent of their degree of risk aversion. We indeed find that the share of agents who choose the comparative scheme is higher under ambiguity than in the case of known output distributions. -- |
| Keywords: | ambiguity aversion,comparative compensation schemes,Ellsberg urn,contract design |
| JEL: | D01 D03 D81 M55 |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:dicedp:55&r=upt |
| By: | Godfrey Charles-Cadogan |
| Abstract: | We introduce a representation theory for risk operations on locally compact groups in a partition of unity on a topological manifold for Markowitz-Tversky-Kahneman (MTK) reference points. We identify (1) risk torsion induced by the flip rate for risk averse and risk seeking behaviour, and (2) a structure constant or coupling of that torsion in the paracompact manifold. The risk torsion operator extends by continuity to prudence and maxmin expected utility (MEU) operators, as well as other behavioural operators introduced by the Italian school. In our erstwhile chaotic dynamical system, induced by behavioural rotations of probability domains, the loss aversion index is an unobserved gauge transformation; and reference points are hyperbolic on the utility hypersurface characterized by the special unitary group SU(n). We identify conditions for existence of harmonic utility functions on paracompact MTK manifolds induced by transformation groups. And we use those mathematical objects to estimate: (1) loss aversion index from infinitesimal tangent vectors; and (2) value function from a classic Dirichlet problem for first exit time of Brownian motion from regular points on the boundary of MTK base topology. |
| Date: | 2012–06 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1206.2665&r=upt |
| By: | Antoni Bosch-Domènech; Joaquim Silvestre |
| Abstract: | Various experimental procedures aimed at measuring individual risk aversion involve a list of pairs of alternative prospects. We first study the widely used method by Holt and Laury (2002), for which we find that the removal of some items from the lists yields a systematic decrease in risk aversion. This bias is quite distinct from other confounds that have been previously observed in the use of the Holt and Laury method. It may be related to empirical phenomena and theoretical developments where better prospects increase risk aversion. Nevertheless, we have also found that the more recent elicitation method due to Abdellaoui et al. (2011), also based on lists, does not display any statistically significant bias when the corresponding items of the list are removed. Our results suggest that methods other than the popular Holt and Laury one may be preferable for the measurement of risk aversion. |
| Date: | 2012–03 |
| URL: | http://d.repec.org/n?u=RePEc:upf:upfgen:1318&r=upt |
| By: | Lionel Page (QUT); David Savage (QUT); Benno Torgler (QUT) |
| Abstract: | This study explores people's risk attitudes after having suffered large real-world losses following a natural disaster. Using the margins of the 2011 Australian floods (Brisbane) as a natural experimental setting, we find that homeowners who were victims of the floods and face large losses in property values are 50% more likely to opt for a risky gamble - a scratch card giving a small chance of a large gain ($500,000) - than for a sure amount of comparable value ($10). This finding is consistent with prospect theory predictions of the adoption of a risk-seeking attitude after a loss. |
| Keywords: | Decision under risk, large losses, natural experiment |
| JEL: | D03 D81 C93 |
| Date: | 2012–06–07 |
| URL: | http://d.repec.org/n?u=RePEc:qut:auncer:2012_6&r=upt |
| By: | Franken, Jason R.V.; Pennings, Joost M.E.; Garcia, Philip |
| Abstract: | Researchers employ various measures of risk attitudes to investigate their relation to market behavior with mixed results. We find that a higher-order global risk attitude construct, developed using survey scales and experiments based on expected utility theory, is related to several marketing alternatives, but does not exhibit substantially greater explanatory power than underlying measures. With few exceptions, scales yield greater significance of risk attitudes for these choices, but experimental measures reveal other insights, e.g., differential attitudes in gain and loss domains. Given recent concerns with experimental measures in the literature, we suggest studies include scales as a low cost supplemental measure. |
| Keywords: | risk behavior, risk attitude, futures and options, forward contracts, marketing contracts, Marketing, Risk and Uncertainty, |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:ags:aaea12:124471&r=upt |
| By: | Yeager, Elizabeth A.; Langemeier, Michael R. |
| Abstract: | This study investigates the impact of risk preferences on economic efficiency scores. Risk averse individuals may be less likely to adopt new technologies and have lower production levels than individuals with other risk preferences. Nonparametric techniques are used to estimate cost and revenue efficiency for a sample of Kansas farms. Each farm had a risk preference score and the scores in the sample ranged from 5 to 86 where a smaller value represents greater risk aversion. Efficiency estimates were first calculated using traditional input and output measures. Efficiency was re-estimated including the inverse risk preference score as a non-discretionary input. Comparisons were made between the characteristics of the farms with an observed efficiency score change and farms without an efficiency score change with the inclusion of inverse risk preferences. As expected, risk preference plays a role in explaining farm inefficiency. Failure to account for risk preferences overstates inefficiency and the improvements in efficiency that can be made. |
| Keywords: | Cost Efficiency, Revenue Efficiency, Risk Preference, Agribusiness, Farm Management, Production Economics, Risk and Uncertainty, C14, D22, D81, |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:ags:aaea12:124012&r=upt |
| By: | Sákovics, József |
| Abstract: | I prove that as long as we allow the marginal utility for money (lambda) to vary between purchases (similarly to the budget) then the quasi-linear and the ordinal budget-constrained models rationalize the same data. However, we know that lambda is approximately constant. I provide a simple constructive proof for the necessary and sufficient condition for the constant lambda rationalization, which I argue should replace the Generalized Axiom of Revealed Preference in empirical studies of consumer behavior. 'Go Cardinals!' It is the minimal requirement of any scientifi c theory that it is consistent with the data it is trying to explain. In the case of (Hicksian) consumer theory it was revealed preference -introduced by Samuelson (1938,1948) - that provided an empirical test to satisfy this need. At that time most of economic reasoning was done in terms of a competitive general equilibrium, a concept abstract enough so that it can be built on the ordinal preferences over baskets of goods - even if the extremely specialized ones of Arrow and Debreu. However, starting in the sixties, economics has moved beyond the 'invisible hand' explanation of how -even competitive- markets operate. A seemingly unavoidable step of this 'revolution' was that ever since, most economic research has been carried out in a partial equilibrium context. Now, the partial equilibrium approach does not mean that the rest of the markets are ignored, rather that they are held constant. In other words, there is a special commodity -call it money - that reflects the trade-offs of moving purchasing power across markets. As a result, the basic building block of consumer behavior in partial equilibrium is no longer the consumer's preferences over goods, rather her valuation of them, in terms of money. This new paradigm necessitates a new theory of revealed preference. |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:edn:sirdps:305&r=upt |
| By: | Alexander Zimper (Department of Economics, University of Pretoria) |
| Abstract: | This paper models the empirical phenomenon of persistent fifty-fifty probability judgements within a dynamic non-additive Savage framework. To this purpose I construct a model of Bayesian learning such that an agent's probability judgement is characterized as the solution to a Choquet expected utility maximization problem with respect to a conditional neo-additive capacity. Only for the non-generic case in which this capacity degenerates to an additive probability measure, the agent's probability judgement coincides with the familiar estimate of a Bayesian statistician who minimizes a quadratic (squared error) loss function with respect to an additive posterior distribution. In contrast, for the generic case in which the capacity is non-additive, the agent's probability judgements converge through Bayesian learning to the unique fuzzy probability measure that assigns a 0.5 probability to any uncertain event. |
| Keywords: | Non-additive measures, Learning, Decision analysis, Economics |
| Date: | 2012–05 |
| URL: | http://d.repec.org/n?u=RePEc:pre:wpaper:201221&r=upt |
| By: | Smeets, Paul (Maastricht University) |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:ner:maastr:urn:nbn:nl:ui:27-29427&r=upt |
| By: | Fabrizio Germano; Peio Zuazo-Garin |
| Abstract: | We extend Aumann's theorem (Aumann, 1987) in deriving correlated equilibria as a consequence of common priors and common knowledge of rationality by explicitly allowing for non-rational behavior. We replace the assumption of common knowledge of rationality with a substantially weaker notion, p-belief of rationality, where agents believe the other agents are rational with probabilities p or more. We show that behavior in this case constitutes a constrained correlated equilibrium of a doubled game satisfying certain p-belief constraints and characterize the topological structure of the resulting set of p-rational outcomes. We establish continuity in the parameters p and show that, for p sufficiently close to one, the p-rational outcomes are close to the correlated equilibria and, with high probability, supported on strategies that survive the iterated elimination of strictly dominated strategies. Finally, we extend Aumann and Dreze's theorem (Aumann and Dreze, 2008) on rational expectations of interim types to the broader p-rational belief systems, and also discuss the case of non-common priors. |
| Keywords: | Correlated equilibrium, approximate common knowledge, bounded rationality, p-rational belief system, common prior, information, noncooperative game |
| JEL: | C72 D82 D83 |
| Date: | 2012–06 |
| URL: | http://d.repec.org/n?u=RePEc:huj:dispap:dp610&r=upt |
| By: | Howard Kunreuther; Geoffrey Heal |
| Abstract: | A principal reason that losses from catastrophic risks have been increasing over time is that more individuals and firms are locating in harm’s way while not taking appropriate protective measures. Several behavioural biases lead decision-makers not to invest in adaptation measures until after it is too late. In an interdependent world with no intervention by the public sector, it may be economically rational for those at risk not to invest in protective measures. Risk management strategies that involve private-public partnerships that address these issues may help in reducing future catastrophic losses. These may include multi-year insurance contracts, well-enforced regulations, third-party inspections, and alternative risk transfer instruments such as catastrophe bonds. |
| JEL: | D62 D80 D85 H20 |
| Date: | 2012–06 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:18136&r=upt |
| By: | ZHOU, Ge |
| Abstract: | This paper discusses the existence of a bubble in the pricing of an asset that pays positive dividends. I show that rational bubbles can exist in a growing economy. The existence of bubbles depends on the relative magnitudes of risk aversion to consumption and to wealth. Furthermore, I examine how an exogenous shock in technology might trigger bubbles. |
| Keywords: | bubbles; the spirit of capitalism; growth |
| JEL: | E44 E20 |
| Date: | 2012–06–11 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:39398&r=upt |
| By: | Strati, Francesco |
| Abstract: | When we face a decision matter we do not face a frozen-time where all keep still while we are making a decision, but the time goes by and the probability distribution keeps moving by new available information. In this paper I want to build up the mathematical framework of a special kind of lottery: the transitional lotteries. This theory could be helpful to give to the decision theory a new key so as to dene a more accurate mental path. In orther to do that we will need a mathematical framework based upon the Kolmogorov operator which will be our transitional object, the core of this kind of lottery. |
| Keywords: | Kolmogorov equations; Decision theory; lotteries |
| JEL: | D81 C02 |
| Date: | 2012–06–11 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:39377&r=upt |
| By: | Pétraud, Jean Paul; Boucher, Stephen R.; Carter, Michael |
| Keywords: | Crop Production/Industries, Risk and Uncertainty, |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:ags:aaea12:124710&r=upt |
| By: | Zhidong Bai (KLASMOE and School of Mathematics and Statistics Northeast Normal University, Department of Statistics and Applied Probability and Risk Management Institute National University of Singapore); Hua Li (Department of Statistics and Applied Probability National University of Singapore); Michael McAleer (Erasmus University Rotterdam,Tinbergen Institute,Kyoto University,Complutense University of Madrid); Wing-Keung Wong (Department of Economics Hong Kong Baptist University) |
| Abstract: | We derive the limiting process of the stochastic dominance statistics for risk averters as well as for risk seekers when the underlying processes might be dependent or independent. We take account of the dependency of the partitions and propose a bootstrap method to decide the critical point. In addition, we illustrate the applicability of the stochastic dominance statistics for both risk averters and risk seekers to analyze the dominance relationship between the Chinese and US stock markets in the entire period as well as the sub-periods before and after the ￣nancial crises, including the internet bubble and the recent sub-prime crisis. The ￣ndings could be used to draw inferences on the preferences of risk averters and risk seekers in investing in the Chinese and US stock markets. The results also enable us to examine whether there is any arbitrage opportunity in these markets and whether these markets are e±cient and investors are rational. |
| Keywords: | Stochastic dominance, risk aversion, risk seeking, test statistic, hypothesis testing. |
| JEL: | C12 G1 G12 G15 |
| Date: | 2012–06 |
| URL: | http://d.repec.org/n?u=RePEc:kyo:wpaper:820&r=upt |
| By: | Strati, Francesco |
| Abstract: | In this paper I shall introduce a new method by which it is possible to study the dynamical decision maker's behaviour. It can be tought of as an application of the S -Linear Algebra of Professor David Carfì, thus this theory it is assumed to be known. I shall focus on the Feynman's propagator and thus the Feynman-Strati propagator. The latter stems form the former. It will be of utmost importance so as to give a meaning to both the evolution and the H-operator by which I shall derive the probability density of this kind of tempered distribution |
| Keywords: | Feynman diagram; Feynman propagator; Green's function; Decision Theory; Lotteries |
| JEL: | C02 D8 |
| Date: | 2012–06–12 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:39399&r=upt |