Utility Models and Prospect Theory
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Utility Models and Prospect Theory2014-10-22Alexander HarinAn expansion in the model space in the context of utility maximization
http://d.repec.org/n?u=RePEc:arx:papers:1410.0946&r=upt
In the framework of an incomplete financial market where the stock price dynamics are modeled by a continuous semimartingale, an explicit first-order expansion formula for the power investor's value function - seen as a function of the underlying market price of risk process - is provided and its second-order error is quantified. Two specific calibrated numerical examples illustrating the accuracy of the method are also given.Kasper Larsen, Oleksii Mostovyi, Gordan \v{Z}itkovi\'c2014-10Discrete choice estimation of risk aversion
http://d.repec.org/n?u=RePEc:upf:upfgen:1443&r=upt
We analyze the use of discrete choice models for the estimation of risk aversion and show a fundamental flaw in the standard random utility model which is commonly used in the literature. Specifically, we find that given two gambles, the probability of selecting the riskier gamble may be larger for larger levels of risk aversion. We characterize when this occurs. By contrast, we show that the alternative random preference approach is free of such problems.Jose Apesteguia, Miguel A. Ballester2014-09Discrete Choice; Structural Estimation; Risk Aversion; Random Utility Models; Random Preference Models.Lexicographic allocations and extreme core payoffs: the case of assignment games
http://d.repec.org/n?u=RePEc:cvh:coecwp:2014/15&r=upt
We consider various lexicographic allocation procedures for coalitional games with transferable utility where the payoffs are computed in an externally given order of the players. The common feature of the methods is that if the allocation is in the core, it is an extreme point of the core. We first investigate the general relationship between these allocations and obtain two hierarchies on the class of balanced games. Secondly, we focus on assignment games and sharpen some of these general relationship. Our main result is the coincidence of the sets of lemarals (vectors of lexicographic maxima over the set of dual coalitionally rational payoff vectors), lemacols (vectors of lexicographic maxima over the core) and extreme core points. As byproducts, we show that, similarly to the core and the coalitionally rational payoff set, also the dual coalitionally rational payoff set of an assignment game is determined by the individual and mixed-pair coalitions, and present an efficient and elementary way to compute these basic dual coalitional values. This provides a way to compute the Alexia value (the average of all lemacols) with no need to obtain the whole coalitional function of the dual assignment game.Nunez, Marina, Solymosi, Tamás2014-10-08assignment game, Alexia valueOn the precautionary motive for savings and prudence in the rank dependent utility framework
http://d.repec.org/n?u=RePEc:ipg:wpaper:2014-597&r=upt
In this paper we deal with the basic two-period consumption saving problem where the first and second period consumption utility, v and u is assumed to be concave re- spectively as usually. We prove that for the rank dependent utility model, prudence is fully characterized by the convexity of u/ and strong pessimism. The paper ends by showing that for a strong risk averse RDU decision maker, strict pessimism allows local weak prudence, whatever the sign of u/// .A.Chateauneuf, G.Lakhnati, E.Langlais2014-09-29RDU Model, Strong Risk Aversion, Pessimism, Prudence and LocalWeak Prudence.Simple Markovian Equilibria in Dynamic Spatial Legislative Bargaining
http://d.repec.org/n?u=RePEc:cer:papers:wp515&r=upt
The paper proves, by construction, the existence of Markovian equilibria in a model of dynamic spatial legislative bargaining. Players bargain over policies in an infinite horizon. In each period, a majority vote takes place between the proposal of a randomly selected player and the status-quo, the policy last enacted. This determines the policy outcome that carries over as the status-quo in the following period; the status-quo is endogenous. Proposer recognition probabilities are constant and discount factors are homogeneous. The construction relies on simple strategies determined by strategic bliss points computed by the algorithm we provide. A strategic bliss point is the policy maximizing the dynamic utility of a player with ample bargaining power. Relative to a bliss point, the static utility ideal, a strategic bliss point is a moderate policy. Moderation is strategic and germane to the dynamic environment; players moderate in order to constrain the future proposals of opponents. Moderation is a strategic substitute; when a player's opponents do moderate, she does not, and when they do not moderate, she does. We prove that the simple strategies induced by the strategic bliss points computed by the algorithm deliver a Stationary Markov Perfect equilibrium. Thus we prove its existence in a large class of symmetric games with more than three players and (possibly with slight adjustment) in any three-player game. Because the algorithm constructs all equilibria in simple strategies, we provide their general characterization, and we show their generic uniqueness. Finally, we analyse how the degree of moderation changes with changes in the model parameters, and we discuss the dynamics of the equilibrium policies.Jan Zapal2014-08dynamic decision-making; endogenous status-quo; spatial bargaining; legislative bargaining;Mean of Ratios or Ratio of Means: statistical uncertainty applied to estimate Multiperiod Probability of Defaul
http://d.repec.org/n?u=RePEc:arx:papers:1409.4896&r=upt
The estimate of a Multiperiod probability of default applied to residential mortgages can be obtained using the mean of the observed default, so called the Mean of ratios estimator, or aggregating the default and the issued mortgages and computing the ratio of their sum, that is the Ratio of means. This work studies the statistical properties of the two estimators with the result that the Ratio of means has a lower statistical uncertainty. The application on a private residential mortgage portfolio leads to a lower probability of default on the overall portfolio by eleven basis points.Matteo Formenti2014-09Turnpike Property and Convergence Rate for an Investment Model with General Utility Functions
http://d.repec.org/n?u=RePEc:arx:papers:1409.7802&r=upt
In this paper we aim to address two questions faced by a long-term investor with a power-type utility at high levels of wealth: one is whether the turnpike property still holds for a general utility that is not necessarily differentiable or strictly concave, the other is whether the error and the convergence rate of the turnpike property can be estimated. We give positive answers to both questions. To achieve these results, we first show that there is a classical solution to the HJB equation and give a representation of the solution in terms of the dual function of the solution to the dual HJB equation. We demonstrate the usefulness of that representation with some nontrivial examples that would be difficult to solve with the trial and error method. We then combine the dual method and the partial differential equation method to give a direct proof to the turnpike property and to estimate the error and the convergence rate of the optimal policy when the utility function is continuously differentiable and strictly concave. We finally relax the conditions of the utility function and provide some sufficient conditions that guarantee the turnpike property and the convergence rate in terms of both primal and dual utility functions.Baojun Bian, Harry Zheng2014-09Measuring Product Type with Dynamics of Online Product Review Variances: A Theoretical Model and the Empirical Applications
http://d.repec.org/n?u=RePEc:net:wpaper:1403&r=upt
A significant body of literature in information systems, marketing, and economics has shown the important implication of the distinction between experience products and search products (â€œproduct typeâ€) on consumer information search, marketplace design, and firm strategy. However, how to empirically measure product types remains a challenge, and this challenge is further complicated by the growth of online commerce and the increasing availability of online reviews that have transformed the nature of many products and altered the traditional perception of these products.
The objective of this research is to propose an online product review-based measure that could accurately reflect consumers’ perception of a product, as search or experience dominated product. Based on the definitions of search and experience products â€” whether information can be easily transferred or not â€” we propose a data-driven method that can be used to infer product type from statistical analyses of online product reviews. Our theoretical analyses indicate that the variance of the ratings should decrease as more consumers rate a pure search product; for experience products however, the variance of the ratings may remain constant or increase depending on the importance of the experience attributes in determining consumer utility. We demonstrate the empirical applications of this approach at the category, product, and attribute levels using product reviews data from Amazon.com, Yelp.com, and Ctrip.com, respectively. In addition, a user study conducted on Amazon Mechanical Turk shows our review-based measure to outperform Nelson’s (1970) product classification, which historically has been the standard in determining product type. Overall, this new measure provides an easy to implement, less subjective and more accurate measure of product type. Therefore, researchers and practitioners can use this measure to better understand how consumers perceive products and to design strategies accordingly.Yili Hong, Pei-yu Chen, Lorin Hitt2014-09product type, online product reviews, user-generated content, data-driven approachCitizen Candidates and Voting Over Incentive-Compatible Nonlinear Income Tax Schedules
http://d.repec.org/n?u=RePEc:van:wpaper:vuecon-sub-14-00011&r=upt
Majority voting over the nonlinear tax schedules proposed by a continuum of citizen candidates is considered. The analysis extends the finite-individual model of RÃ¶ell (unpublished manuscript, 2012). Each candidate proposes the tax schedule that is utility maximal for him subject to budget and incentive constraints. Each of these schedules is a combination of the maxi-min and maxi-max schedules along with a region of bunching in a neighborhood of the proposer's type. Techniques introduced by Vincent and Mason (1967, NASA Contractor Report CR-744) are used to identify the bunching region. As in RÃ¶ell's model, it is shown that individual preferences over these schedules are single-peaked, so the median voter theorem applies. In the majority rule equilibrium, marginal tax rates are negative for low-skilled individuals and positive for high-skilled individuals except at the endpoints of the skill distribution where they are typically zero.Craig Brett, John A Weymark2014-09-26bunching, citizen candidates, ironing, majority voting, nonlinear income taxation