
on Utility Models and Prospect Theory 
By:  James C. Cox; Vjollca Sadiraj 
Abstract:  Theories of decision under risk that challenge expected utility theory model risk attitudes at least partly with transformation of probabilities. We explain how attributing risk aversion (partly or wholly) to attitude towards probabilities, can produce extreme probability distortions that imply paradoxical risk aversion. 
Keywords:  risk aversion, probability transformation, calibration, reference dependence, loss aversion 
Date:  2011–06 
URL:  http://d.repec.org/n?u=RePEc:exc:wpaper:201110&r=upt 
By:  James C. Cox; Vjollca Sadiraj; Ulrich Schmidt 
Abstract:  Experiments on choice under risk typically involve multiple decisions by individual subjects. The choice of mechanism for selecting decision(s) for payoff is an essential design feature that is often driven by appeal to the isolation hypothesis or the independence axiom. We report two experiments with 710 subjects. Experiment 1 provides the first simple test of the isolation hypothesis. Experiment 2 is a crossed design with six payoff mechanisms and five lottery pairs that can elicit four paradoxes for the independence axiom and dual independence axiom. The crossed design discriminates between: (a) behavioral deviations from postulated properties of payoff mechanisms; and (b) behavioral deviations from theoretical implications of alternative decision theories. Experiment 2 provides tests of the isolation hypothesis and four paradoxes. It also provides data for tests for portfolio effect, wealth effect, reduction, adding up, and crosstask contamination. Data from Experiment 2 suggest that a new mechanism introduced herein may be less biased than random selection of one decision for payoff 
Keywords:  isolation, mechanisms, paradoxes, independence, dual independence, crosstask contamination, portfolio effect, wealth effect, reduction, addingup 
JEL:  C91 D81 
Date:  2011–06 
URL:  http://d.repec.org/n?u=RePEc:kie:kieliw:1712&r=upt 
By:  Markus Mocha; Nicholas Westray 
Abstract:  This article studies the sensitivity of the power utility maximization problem with respect to the investor's relative risk aversion, the statistical probability measure, the investment constraints and the market price of risk. We extend previous descriptions of the dual domain then exploit the link between the constrained utility maximization problem and continuous semimartingale quadratic BSDEs to reduce questions on sensitivity to results on stability for such equations. This then allows us to prove appropriate convergence of the primal and dual optimizers in the semimartingale topology. 
Date:  2011–07 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1107.0190&r=upt 
By:  Koch, Alexander K. (University of Aarhus); Nafziger, Julia (University of Aarhus) 
Abstract:  We model how people formulate and evaluate goals to overcome selfcontrol problems. People often attempt to regulate their behavior by evaluating goalrelated outcomes separately (in narrow psychological accounts) rather than jointly (in a broad account). To explain this evidence, our theory of endogenous narrow or broad psychological accounts combines insights from the literatures on goals and mental accounting with models of expectationsbased referencedependent preferences. By formulating goals the individual creates expectations that induce reference points for task outcomes. These goalinduced reference points make substandard performance psychologically painful and motivate the individual to stick to his goals. How strong the commitment to goals is depends on the type of psychological account. We provide conditions when it is optimal to evaluate goals in narrow accounts. The key intuition is that broad accounts make decisions or risks in different tasks substitutes and thereby create incentives to deviate from goals. Model extensions explore the robustness of our results to different timing assumptions and goal and account revision. 
Keywords:  quasihyperbolic discounting, referencedependent preferences, loss aversion, selfcontrol, mental accounting, goals 
JEL:  A12 C70 D81 D91 
Date:  2011–06 
URL:  http://d.repec.org/n?u=RePEc:iza:izadps:dp5802&r=upt 
By:  Burks, Stephen V. (University of Minnesota, Morris); Carpenter, Jeffrey P. (Middlebury College); Goette, Lorenz (University of Lausanne); Rustichini, Aldo (University of Minnesota) 
Abstract:  Economists and psychologists have devised numerous instruments to measure time preferences and have generated a rich literature examining the extent to which time preferences predict important outcomes; however, we still do not know which measures work best. With the help of a large sample of nonstudent participants (truck driver trainees) and administrative data on outcomes, we gather four different time preference measures and test the extent to which they predict both on their own and when they are all forced to compete headtohead. Our results suggest that the now familiar (β, δ) formulation of present bias and exponential discounting predicts best, especially when both parameters are used. 
Keywords:  time preference, impatience, discounting, present bias, field experiment, trucker 
JEL:  C93 D90 
Date:  2011–06 
URL:  http://d.repec.org/n?u=RePEc:iza:izadps:dp5808&r=upt 
By:  Christoph Frei; Markus Mocha; Nicholas Westray 
Abstract:  This article studies quadratic semimartingale BSDEs arising in power utility maximization when the market price of risk is of BMO type. In a Brownian setting we provide a necessary and sufficient condition for the existence of a solution but show that uniqueness fails to hold in the sense that there exists a continuum of distinct squareintegrable solutions. This feature occurs since, contrary to the classical Ito representation theorem, a representation of random variables in terms of stochastic exponentials is not unique. We study in detail when the BSDE has a bounded solution and derive a new dynamic exponential moments condition which is shown to be the minimal sufficient condition in a general filtration. The main results are complemented by several interesting examples which illustrate their sharpness as well as important properties of the utility maximization BSDE. 
Date:  2011–07 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1107.0183&r=upt 
By:  Birendra K. Rai1; Chiu Ki So; Aaron Nicholas 
Abstract:  This paper is modeled as a hypothetical first lecture in a graduate Microeconomics or Mathematical Economics Course. We start with a detailed scrutiny of the notion of a utility function to motivate and describe the common patterns across Mathematical concepts and results that are used by economists. In the process we arrive at a classification of mathematical terms which is used to state mathematical results in economics. The usefulness of the classification scheme is illustrated with the help of a discussion of fixedpoint theorems and Arrow's impossibility theorem. Several appendices provide a stepwise description of some mathematical concepts often used by economists and a few useful results in microeconomics. 
Keywords:  Mathematics, Set theory, Utility function, Arrow's impossibility theorem 
Date:  2011–06 
URL:  http://d.repec.org/n?u=RePEc:mos:moswps:201102&r=upt 