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on Utility Models and Prospect Theory |
| By: | Carole Bernard; Franck Moraux; Ludger Rueschendorf; Steven Vanduffel |
| Abstract: | Most decision theories including expected utility theory, rank dependent utility theory and the cumulative prospect theory assume that investors are only interested in the distribution of returns and not about the states of the economy in which income is received. Optimal payoffs have their lowest outcomes when the economy is in a downturn, and this is often at odds with the needs of many investors. We introduce a framework for portfolio selection that permits to deal with state-dependent preferences. We are able to characterize optimal payoffs in explicit form. Some applications in security design are discussed in detail. We extend the classical expected utility optimization problem of Merton to the state-dependent situation and also give some stochastic extensions of the target probability optimization problem. |
| Date: | 2013–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1308.6465&r=upt |
| By: | Marcello Basili; Luca Pratelli |
| Abstract: | We consider an aggregation scheme of opinions expressed through different probability distributions or multiple priors decision model. The decision-maker adopts entropy maximization as a measure of risk diversification and a rational form of prudence for valuing uncertain outcomes. We show a new aggregation rule formalization based on the idea that the decision-maker has a more reliable set of outcomes called ordinary and two fat tails that include more ambiguous and extreme events. |
| Keywords: | Ambiguity, Aggregation, Entropy, Multiple Priors, Quantiles |
| JEL: | D81 |
| Date: | 2013–06 |
| URL: | http://d.repec.org/n?u=RePEc:usi:wpaper:677&r=upt |
| By: | Guo, Xu; Wong, Wing-Keung; Zhu, Lixing |
| Abstract: | This paper first extends the theory of almost stochastic dominance (ASD) to the first four orders. We then establish some equivalent relationships for the first four orders of the ASD. Using these results, we prove formally that the ASD definition modified by Tzeng et al.\ (2012) does not possess any hierarchy property. Thereafter, we conclude that when the first four orders of ASD are used in the prospects comparison, risk-averse investors prefer the one with positive gain, smaller variance, positive skewness, and smaller kurtosis. This information, in turn, enables decision makers to determine the ASD relationship among prospects when they know the moments of the prospects. At last, we discuss the necessary and sufficient conditions for different orders the ASD and the moments of the prospects. |
| Keywords: | Stochastic dominance; almost stochastic dominance; risk aversion, mean, variance, skewness |
| JEL: | C0 D81 G11 |
| Date: | 2013–08–21 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:49274&r=upt |
| By: | Marcello Basili; Alain Chateauneuf |
| Abstract: | The paper defines a consensus distribution with respect to experts’ opinions by a multiple quantile utility model. The paper points out that the Steiner Point is the representative consensus probability. The new rule of experts’ opinions aggregation, that can be evaluated by the Shapley value in a simple way, is prudential and coherent. |
| Keywords: | Ambiguity, Aggregation, Steiner Point, Multiple Priors, Quantiles |
| Date: | 2013–06 |
| URL: | http://d.repec.org/n?u=RePEc:usi:wpaper:676&r=upt |
| By: | Hao Liu (CoFE, University of Konstanz, Germany); Winfried Pohlmeier (CoFE, University of Konstanz, Germany; ZEW, Germany; RCEA, Italy) |
| Abstract: | This paper analyzes the estimation risk of efficient portfolio selection. We use the concept of certainty equivalent as the basis for a well-defined statistical loss function and a monetary measure to assess estimation risk. For given risk preferences we provide analytical results for different sources of estimation risk such as sample size, dimension of the portfolio choice problem and correlation structure of the return process. Our results show that theoretically sub-optimal portfolio choice strategies turn out to be superior once estimation risk is taken into account. Since estimation risk crucially depends on risk preferences, the choice of the estimator for a given portfolio strategy becomes endogenous. We show that a shrinkage approach accounting for estimation risk in both, mean and covariance of the return vector, is generally superior to simple theoretically suboptimal strategies. Moreover, focusing on just one source of estimation risk, e.g. risk reduction in covariance estimation, can lead to suboptimal portfolios. |
| Keywords: | efficient portfolio, estimation risk, certainty equivalent, shrinkage |
| JEL: | G11 G12 G17 |
| Date: | 2013–08 |
| URL: | http://d.repec.org/n?u=RePEc:rim:rimwps:47_13&r=upt |
| By: | Nathan Berg (Department of Economics, University of Otago, New Zealand); G. Biele; Gerd Gigerenzer |
| Abstract: | When economists' subjective beliefs about the sensitivity and positive predictive value of the Prostate Specific Antigen (PSA) test are internally consistent (i.e., satisfying Bayes' Rule), their beliefs about prostate cancer risk are less accurate than among those with inconsistent beliefs. Using a loss function framework, we investigate but cannot find evidence that inconsistent beliefs lead to inaccuracy, different PSA decisions, or economic losses. Economists' PSA decisions appear to depend much more on the advice of doctors and family members than on beliefs about cancer risks and the pros/cons of PSA testing, which have little to no joint explanatory power. |
| Date: | 2013–04 |
| URL: | http://d.repec.org/n?u=RePEc:otg:wpaper:1308&r=upt |
| By: | William J. McCausland; A.A.J. Marley |
| Abstract: | We complete the development of a testing ground for axioms of discrete stochastic choice. Our contribution here is to develop new posterior simulation methods for Bayesian inference, suitable for a class of prior distributions introduced by McCausland and Marley (2013). These prior distributions are joint distributions over various choice distributions over choice sets of different sizes. Since choice distributions over different choice sets can be mutually dependent, previous methods relying on conjugate prior distributions do not apply. We demonstrate by analyzing data from a previously reported experiment and report evidence for and against various axioms. |
| Keywords: | Random utility, discrete choice, Bayesian inference, MCMC |
| JEL: | C11 C35 C53 D01 |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:mtl:montec:07-2013&r=upt |
| By: | Robert Baumann (Department of Economics, College of the Holy Cross); Justin Svec (Department of Economics, College of the Holy Cross) |
| Abstract: | In this paper, we examine how candidate uncertainty affects the policy platforms chosen in a uni-dimensional, two candidate Downsian spatial model. The candidates, we assume, do not know the true distribution of voters. Following the robust control literature, candidates respond to this uncertainty by applying a max-min operator to their optimization problem. This approach, consistent with findings within the behavioral economics literature, protects the candidate by ensuring that her expected utility never falls too far, regardless of the true voter distribution. We show that this framework produces policy convergence between the two candidates but there is a multiplicity of possible policy platforms upon which the candidates could settle, some of which could be quite distant from the median voter. These results are robust to the timing of the game and the level of uncertainty faced by the candidates. We argue that our model explains drift, which is our term for changing political beliefs over time. While drift may be caused by shifting attitudes or demographics, we show that drift could also be the result of candidate uncertainty. |
| Keywords: | Robust control, candidate uncertainty, voting, spatial model |
| JEL: | H00 D78 D84 |
| Date: | 2013–08 |
| URL: | http://d.repec.org/n?u=RePEc:hcx:wpaper:1306&r=upt |
| By: | Bolle, Friedel; Costard, Jano |
| Abstract: | In the Solidarity game lucky winners of a lottery can transfer part of their income to unlucky losers. Will losers get smaller transfers if they can be assumed to be responsible for their zero income because they have chosen riskier lotteries? Or will risk-lovers and riskaverters favor those who made the same risk-choice, leading to larger transfers within rather than between the risk-groups? While there is support for both motives in the literature, in an experiment we find that the effect of holding people responsible for their actions is overcome by behavior guided by in-group favoritism based on different levels of risk-taking. This behavior is successfully described by a variant of the social utility function suggested by Cappelen et al. (2013). -- Im Solidaritätsspiel können die glücklichen Gewinner einer Lotterie einen Teil ihres Gewinns den unglücklichen Verlierern überlassen. Erhalten die Verlierer eine geringere Kompensation, wenn sie dafür verantwortlich gemacht werden können, dass sie leer ausgingen, weil sie sich für eine riskantere Lotterie entschieden hatten? Oder bevorzugen risikofreudige und risikoscheue Spieler diejenigen, die sich für das jeweils gleiche Risikoniveau entschieden hatten? Während es in der Literatur Argumente für beide Motive gibt, zeigt sich im Experiment, dass Verlierer mehr Solidarität erfahren, wenn sie die gleiche Risikoentscheidung getroffen haben wie der Gewinner und dass damit das Motiv Spieler für ihre Entscheidung verantwortlich zu machen in den Hintergrund treten kann. Dieses Verhalten kann erfolgreich durch eine Variante der social utility function, wie sie von Cappelen et al. (2013) vorgeschlagen wurde, erklärt werden. |
| Keywords: | Risky Behaviour,Solidarity,Responsibility,In-Group Favoritism |
| JEL: | D3 D8 |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:wzbeoc:spii2013308&r=upt |
| By: | Eizo Akiyama (Faculty of Engineering, Information and Systems, University of Tsukuba - University of Tsukuba); Nobuyuki Hanaki (AMSE - Aix-Marseille School of Economics - Aix-Marseille Univ. - Centre national de la recherche scientifique (CNRS) - École des Hautes Études en Sciences Sociales [EHESS] - Ecole Centrale Marseille (ECM), IUF - Institut Universitaire de France - Ministère de l'Enseignement Supérieur et de la Recherche Scientifique); Ryuichiro Ishikawa (Faculty of Engineering, Information and Systems, University of Tsukuba - University of Tsukuba) |
| Abstract: | To what extent is the observed mis-pricing in experimental asset markets caused by strategic uncertainty (SU) and by individual bounded rationality (IBR)? We address this question by comparing subjects initial price forecasts in two market environments - one with six human traders, and the other with one human and five computer traders. We find that both SU and IBR account equally for the median initial forecasts deviation from the fundamental values. The effect of SU is greater for subjects with a perfect score in the Cognitive Reflection Test, and it is not significant for those with low scores. |
| Keywords: | bounded rationality; strategic uncertainty; experiment; asset markets; computer traders; cognitive reflection test |
| Date: | 2013–08 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:halshs-00854513&r=upt |
| By: | Su, EnDer |
| Abstract: | This paper studies the risk hedging between stock index and underlying futures. The hedging ratios are optimized using the mean-variance utility function as considering the hedging cost. The trend of returns and variance are estimated by the model of regime switch on both vector autoregression (VAR) and GARCH(1,1) compared to three restricted models: VAR switch only, GARCH(1,1) switch only, and no switch. The hedge portfolio is constructed by Morgan Stanley Taiwan Index (MSTI) and Singapore Traded MSTI futures. The hedge horizon is set as a week to reduce the hedging cost and the weekly in-sample data cover from 08/09/2001 to 05/31/2007. The rolling window technique is used to evaluate the hedge performances of out-of-sample period spanning subprime, Greek debt, and post-risk durations. The subprime period indeed is evidenced very vital to achieve the hedge performance. All models perform surprisingly far above average during subprime period. The hedge ratios indeed are the tradeoff between maximum expected return and minimum variance. It is demonstrated challenging for all models to increase returns and reduce risk together. The hedge context is further classified into four hedge states: uu, ud, du, and dd (u and d denote respectively usual and down) using the state probabilities of series. The regime switch models are found to have much greater wealth increase when in dd state. It is decisive to hedge risk in dd state when volatility is extensively higher as observed recurrently in subprime period. Remarkably, the trend switch is found having larger wealth increase while the volatility switch is not found prominent between models. While the no switch model has larger utility increase in uu state as most observed in Greek debt or post risk period, its performance is far below average like other models. |
| Keywords: | stock index, regime switch, hedging cost, hedging ratio |
| JEL: | C13 C51 |
| Date: | 2013–01–09 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:49190&r=upt |
| By: | Redzo Mujcic (School of Economics, The University of Queensland); Paul Frijters (School of Economics, The University of Queensland) |
| Abstract: | We present a simple model of status-seeking over multiple socioeco- nomic domains by introducing the concept of conspicuous health as an argument in the utility function, in addition to the well-established conspicuous consumption term. We explore the implications of such a utility function for optimal income taxation, where we show an in- crease in concerns for conspicuous health to have an opposite effect on the marginal tax rate, compared to an increase in concerns for conspic- uous consumption. Using life satisfaction panel data from Australia, along with an improved measure of exogenous reference groups (that accounts for the ‘time era’ of respondents), we find evidence of a com- parison health effect. |
| Date: | 2013–08–20 |
| URL: | http://d.repec.org/n?u=RePEc:qld:uq2004:483&r=upt |