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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 conditional expectation increasing or decreasing. We show that our order of cross Ross risk aversion is equivalent to the order of partial risk premium, while our index of decreasing cross Ross risk aversion is equivalent to 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, Dependent background risk, Partial risk premium, Decreasing cross Ross risk aversion, n-switch utility function |
| JEL: | D81 |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:lvl:lacicr:1211&r=upt |
| By: | Traeger, Christian P. (University of California, Berkeley. Dept of agricultural and resource economics) |
| Abstract: | The paper analyzes the discount rate under uncertainty. The analysis complements the probabilistic characterization of uncertainty by a measure of confidence. Special cases of the model comprise discounting under smooth ambiguity aversion as well as discounting under a disentanglement of risk aversion from aversion to intertemporal substitution. The paper characterizes the general class of preferences for which uncertainty implies a reduction of the discount rate. It also characterizes how the more comprehensive description of uncertainty changes the discount rate with respect to the standard model. The paper relates different results in the literature by switching between different risk measures. It presents a parametric extension of the Ramsey discounting formula that takes into account confidence into future growth estimates and a measure of aversion to the lack of confidence. If confidence decreases in the futurity of the growth forecast, the discount rates have a falling term structure even in the case of an iid growth process. |
| Keywords: | uncertainty, discounting, climate change, ambiguity, confidence, subjective beliefs, prudence, pessimism, expected utility, intertemporal substitutability, intertemporal risk aversion |
| JEL: | D61 Q54 D81 D90 |
| Date: | 2011–06 |
| URL: | http://d.repec.org/n?u=RePEc:are:cudare:1117r&r=upt |
| By: | Crès, Hervé (Département d'économie); Gilboa, Itzhak; Vieille, Nicolas |
| Abstract: | Experts are asked to provide their advice in a situation of uncertainty. They adopt the decision maker’s utility function, but each has a potentially different set of prior probabilities, and so does the decision maker. The decision maker and the experts maximize the minimal expected utility with respect to their sets of priors. We show that a natural Pareto condition is equivalent to the existence of a set Λ of probability vectors over the experts, interpreted as possible allocations of weights to the experts, such that (i) the decision maker’s set of priors is precisely all the weighted-averages of priors, where an expert’s prior is taken from her set and the weight vector is taken from Λ; (ii) the decision maker’s valuation of an act is the minimal weighted valuation, over all weight vectors in Λ, of the experts’ valuations. |
| Keywords: | Aggregation of opinions, Ambiguity, Multiple priors; |
| JEL: | D7 D8 |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:ner:sciepo:info:hdl:2441/eu4vqp9ompqllr09iepso50rh&r=upt |
| By: | Sheremeta, Roman M. (Chapman University); Wu, Steven Y. (Purdue University) |
| Abstract: | We use experiments to test comparative statics predictions of canonical tournament theory. Both the roles of principal and agent are populated by human subjects, allowing us to test predictions for both incentive responses and optimal tournament design. Consistent with theory, we observed an incentive effect from raising the winner's prize. However, we also observed several empirical puzzles that appeared to contradict theory. Controlling for social preferences did not resolve the puzzles, although social preferences do influence behavior. It turns out that the puzzles can be explained by the canonical model once the textbook assumption of separable agent utility is relaxed. |
| Keywords: | tournaments, experiment, social preferences, contract theory |
| JEL: | D03 D82 D86 M52 M55 |
| Date: | 2012–01 |
| URL: | http://d.repec.org/n?u=RePEc:iza:izadps:dp6304&r=upt |
| By: | Leuermann, Andrea; Necker, Sarah |
| Abstract: | This study investigates whether the willingness to take income risks revealed by occupational choice is transmitted from parents to their children. Using data from the German Socio-Economic Panel (SOEP), we find that fathers' riskiness of job is a significant determinant of children's occupational risk, in particular sons' (excluding parent-child pairs with identical occupations). This is the first piece of evidence for intergenerational transmission of risk attitudes relying on real world behavior. It shows that not only individuals' own assessments of their risk attitudes correlate across generations (found by previous studies) but also risk preferences shown in exactly the same situation. -- |
| Keywords: | risk preferences,intergenerational transmission,occupational choice |
| JEL: | D12 D81 J24 |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:aluord:114&r=upt |
| By: | Forges, Françoise; Iehlé, Vincent |
| Abstract: | According to a minimalist version of Afriat’s theorem, a consumer behaves as a utility maximizer if and only if a feasibility matrix associated with his choices is cyclically consistent. An ”essential experiment” consists of observed consumption bundles (x1,xn) and a feasibility matrix α. Starting with a standard experiment, in which the economist has specific budget sets in mind, we show that the necessary and sufficient condition for the existence of a utility function rationalizing the experiment, namely, the cyclical consistency of the associated feasibility matrix, is equivalent to the existence, for any budget sets compatible with the deduced essential experiment, of a utility function rationalizing them (and typically depending on them). In other words, the conclusion of the standard rationalizability test, in which the economist takes budget sets for granted, does not depend on the full specification of the underlying budget sets but only on the essential data that these budget sets generate. Starting with an essential experiment (x1,...,xn;α), we show that the cyclical consistency of α, together with a further consistency condition involving both (x1,...,xn) and α, guarantees that the essential experiment is rationalizable almost robustly, in the sense that there exists a single utility function which rationalizes at once almost all budget sets which are compatible with (x1,...,xn;α). The conditions are also trivially necessary. |
| Keywords: | Afriat’s theorem; budget sets; cyclical consistency; rational choice; revealed preference |
| JEL: | D11 C81 |
| Date: | 2012–02–07 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:36519&r=upt |
| By: | Uwe Dulleck (QUT); Andreas Loffler |
| Abstract: | Risk aversion in game theory is usually modelled using expected utility, which has been critized early on leading to an extensive literature on generalized expected utility. In this paper we are first to apply μ-σ theory to the analysis of (static) games. μ-σ theory is widely accepted in the finance literature, using it allows us to study the effect on uncertainty endogenous to the game, i.e. mixed equilibria. In particular, we look at the case of linear μ-σ utility functions and determine the best response strategy. In the case of 2x2- and NxM-games we are able to characterize all mixed equilibria. |
| Date: | 2012–01–13 |
| URL: | http://d.repec.org/n?u=RePEc:qut:auncer:2012_1&r=upt |
| By: | Lotz, Aileen; Gosselin, Pierre |
| Abstract: | This paper advocates that some limits of the rational agent hypothesis result from the improper assumption that one individual should be modeled as a single rational agent. We model an individual composed of two autonomous and interacting structures, conscious and unconscious. Each agent utility form depends both on external signals and other structures' actions. The perception of the signal depends on its recipient and its grid of interpretation. We study both the static and dynamic version of this interaction mechanism. We show that the dynamics may display instability, depending on the structures interactions'strength. However, if unconscious has a strategic advantage, greater stability is reached. By manipulating other structuresgoals, the strategic agent can lead the whole system to an equilibrium closer to its own optimum. This result shows that some switch in the consciousobjective can appear. Behaviors that can't be explained with a single utility can thus be rational if we add a rational unconscious agent. Our results justify our hypothesis of a rational interacting unconscious. It supports the widening of the notion of rationality to multi-rationnality in interaction. |
| Keywords: | dual agent; conscious and unconscious; rationality; multi-rationality; emotions; choices and preferences; multi-agent model; consistency; |
| JEL: | D70 D01 D87 |
| Date: | 2012–02–15 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:36697&r=upt |
| By: | Stephen Satchell (Trinity College, University of Cambridge); Susan Thorp (Finance Discipline Group, UTS Business School, University of Technology, Sydney); Oliver Williams (Scalpel Research and Kings College, University of Cambridge) |
| Abstract: | We derive and estimate the optimal disbursement from an infinitely-lived charitable trust with an Epstein-Zin-Weil utility function, given general Markovian returns to wealth. We analyze two special cases: where spending is a power function of last period's wealth and the endowment uses 'payout smoothing'. Via nonlinear least squares, we estimate the optimal spending rate and the elasticity of intertemporal substitution for a trust with a typical diversified portfolio and for a portfolio of hedge funds. Finally, we use maximum entropy methods to characterize the returns distribution of a trust whose spending plan conforms with the optimality condition. |
| Keywords: | Intertemporal choice; Elasticity of intertemporal substitution; Moving average |
| JEL: | G23 D81 D91 E21 |
| Date: | 2012–01–01 |
| URL: | http://d.repec.org/n?u=RePEc:uts:rpaper:300&r=upt |
| By: | Gürtler, Marc; Stolpe, Julia |
| Abstract: | We extend the continuous Cumulative Prospect Theory (CPT) by considering piecewise con-tinuous distributions with a finite number of jump discontinuities. Such distributions are rele-vant in practice, for example, within the framework of financial engineering since cash flow distributions of most types of derivatives are only piecewise continuous. In addition, we ex-pand the model with a (piecewise) continuous version of hedonic framing which is, until now, only available in a discrete model setting. We show how to apply the model to a broad class of structured products. Finally, we apply Prospect Theory (PT), CPT, and expected utility theory to a set of different real-life certificates with piecewise continuous and discrete distributions in order to analyze whether there are any significant differences between the theories, and which theory is able to explain the demand behavior of a market participant best. As a result, we recommend the use of the piecewise continuous version of CPT to design products within the framework of behavioral financial engineering. -- |
| Keywords: | Continuous Cumulative Prospect Theory,Continuous Hedonic Framing,Behavioral Finance,Financial Engineering |
| JEL: | G31 G32 G35 |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:tbsifw:if37v1&r=upt |
| By: | Giuseppe Cappelletti (Bank of Italy) |
| Abstract: | Data from the Italian Survey of Households Income and Wealth (SHIW) are used to study portfolio allocations change in response to fluctuations in wealth. In particular I test for the prediction of models with habit formation that changes in liquid wealth will affect households' risk aversion and risky asset investment. After controlling for the decision to enter and leave the risky asset market, I find, in contrast with other studies (Brunnermeier and Nagel, 2008 and Chiappori and Paiella, 2008), that changes in wealth do help to explain changes in asset allocation. |
| Keywords: | portfolio allocation, risk aversion, habit-formation |
| JEL: | D14 D31 G11 |
| Date: | 2012–01 |
| URL: | http://d.repec.org/n?u=RePEc:bdi:wptemi:td_845_12&r=upt |