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on Utility Models and Prospect Theory |
| By: | David Johnstone; Dennis Lindley |
| Abstract: | The model of rational decision-making in most of economics and statistics is expected utility theory (EU) axiomatised by von Neumann and Morgenstern, Savage and others. This is less the case, however, in financial economics and mathematical finance, where investment decisions are commonly based on the methods of mean-variance (MV) introduced in the 1950s by Markowitz. Under the MV framework, each available investment opportunity ("asset") or portfolio is represented in just two dimensions by the ex ante mean and standard deviation $(\mu,\sigma)$ of the financial return anticipated from that investment. Utility adherents consider that in general MV methods are logically incoherent. Most famously, Norwegian insurance theorist Borch presented a proof suggesting that two-dimensional MV indifference curves cannot represent the preferences of a rational investor (he claimed that MV indifference curves "do not exist"). This is known as Borch's paradox and gave rise to an important but generally little-known philosophical literature relating MV to EU. We examine the main early contributions to this literature, focussing on Borch's logic and the arguments by which it has been set aside. |
| Date: | 2013–06 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1306.2728&r=upt |
| By: | Harin, Alexander |
| Abstract: | A theorem of existence of the non-zero restrictions for the mean of a function on a finite numerical segment at a non-zero dispersion of the function is proved. The theorem has an applied character. It is aimed to be used in the probability theory and statistics and further in economics. Its ultimate aim is to help to answer the Aczél-Luce question whether W(1)=1 and to explain, at least partially, the well-known problems and paradoxes of the utility theory, such as the underweighting of high and the overweighting of low probabilities, the Allais paradox, the four-fold pattern paradox, etc., by purely mathematical methods. |
| Keywords: | utility; utility theory; probability; uncertainty; decisions; economics; Prelec; probability weighting; Allais paradox; risk aversion; |
| JEL: | C0 C02 C1 D81 G22 |
| Date: | 2013–06–11 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:47559&r=upt |
| By: | Massimo Guidolin; Hening Liuz |
| Abstract: | We examine asset allocation decisions under smooth ambiguity aversion when an investor has a prior degree of belief in an asset pricing model (e.g., the domestic CAPM). Different from the Bayesian portfolio approach, in our model the investor separately relies on the conditional distribution of returns and on the posterior over uncertain parameters to make asset allocation decisions, rather than on the predictive distribution of returns that integrates priors and likelihood information in a single distribution. This is a key feature implied by smooth ambiguity preferences. We find that in the perspective of US investors, ambiguity aversion can generate strong home bias in their equity holdings, regardless of their belief in the domestic CAPM or of their degree of risk aversion. Our results extend and become stronger under regime-switching investment opportunities. JEL Classification: C61; D81; G11. Keywords: Ambiguity aversion, Bayesian portfolio analysis, CAPM, Smooth ambiguity. |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:igi:igierp:483&r=upt |
| By: | Emel Filiz-Ozbay; Jonathan Guryan; Kyle Hyndman; Melissa Schettini Kearney; Erkut Y. Ozbay |
| Abstract: | This paper presents the results of a laboratory experiment designed to investigate whether the option of a Prize Linked Savings (PLS) product alters the likelihood that subjects choose to delay payment. By comparing PLS and standard savings products in a controlled way, we find strong evidence that a PLS payment option leads to greater rates of payment deferral than does a straightforward interest payment option of the same expected value. The appeal of the PLS option is strongest among men, self-reported lottery players, and subjects with low bank account balances. We use the results of our experiment to structurally estimate the parameters of the decision problem governing time preference, risk aversion, and probability weighting. We employ the parameter estimates in a series of policy simulations that compare the relative effectiveness of PLS products as compared to standard savings products. |
| JEL: | D03 D14 D81 G11 |
| Date: | 2013–06 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:19130&r=upt |
| By: | Antonio Nicita (Department of Economics and Law, La Sapienza University of Rome.); Matteo Rizzolli (Free University of Bozen) |
| Abstract: | The standard model of optimal deterrence predicts that the probability of wrongful conviction of the innocent is, at the margin, as detrimental to deterrence as the probability of wrongful acquittal of guilty individuals. We extend the model in several directions: using expected utility as well as non-expected utility to consider the role of risk aversion, non-linear probability weighting and loss aversion. We also consider how relevant emotions such as guilt, shame and indignation play out. Several of these factors support the intuition that wrongful convictions of the innocent do have a larger detrimental impact on deterrence and thus the policy implications are reconciled with the widely shared maxim in dubio pro reo. We then draw some theoretical implications such as a novel justification for the different standards of proof in criminal vs civil law as well as other policy implications. |
| Keywords: | wrongful convictions, Type I errors, wrongful acquittals, Type II errors, evidence, optimal under-deterrence, behavioral economics, risk aversion, loss aversion, prospect theory, prelec function |
| JEL: | K14 K41 K42 |
| Date: | 2013–06 |
| URL: | http://d.repec.org/n?u=RePEc:bzn:wpaper:bemps04&r=upt |