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on Utility Models and Prospect Theories |
| By: | Stefan Ankirchner; Steffen Dereich; Peter Imkeller |
| Abstract: | The background for the general mathematical link between utility and information theory investigated in this paper is a simple financial market model with two kinds of small traders: less informed traders and insiders, whose extra information is represented by an enlargement of the other agents’ filtration. The expected logarithmic utility increment, i.e. the difference of the insider’s and the less informed trader’s expected logarithmic utility is described in terms of the information drift, i.e. the drift one has to eliminate in order to perceive the price dynamics as a martingale from the insider’s perspective. On the one hand, we describe the information drift in a very general setting by natural quantities expressing the probabilistic better informed view of the world. This on the other hand allows us to identify the additional utility by entropy related quantities known from information theory. In particular, in a complete market in which the insider has some fixed additional information during the entire trading interval, its utility increment can be represented by the Shannon information of his extra knowledge. For general markets, and in some particular examples, we provide estimates of maximal utility by information inequalities. |
| Keywords: | enlargement of filtration, logarithmic utility, utility maximization, heterogeneous information, insider model, Shannon information, information difference, entropy, differential entropy |
| JEL: | C61 D82 |
| Date: | 2005–05 |
| URL: | http://d.repec.org/n?u=RePEc:hum:wpaper:sfb649dp2005-030&r=upt |
| By: | Burkhard C. Schipper (Department of Economics, University of California, Davis, One Shields Avenue, Davis, CA 95616, USA. bcschipper@ucdavis.com) |
| Abstract: | We provide an evolutionary foundation to evidence that in some situations humans maintain optimistic or pessimistic attitudes towards uncertainty and are ignorant to relevant aspects of the environment. Players in strategic games face Knightian uncertainty about opponents’ actions and maximize individually their Choquet expected utility. Our Choquet expected utility model allows for both an optimistic or pessimistic attitude towards uncertainty as well as ignorance to strategic dependencies. An optimist (resp. pessimist) overweights good (resp. bad) outcomes. A complete ignorant never reacts to opponents’ change of actions. With qualifications we show that optimistic (resp. pessimistic) complete ignorance is evolutionary stable / yields a strategic advantage in submodular (resp. supermodular) games with aggregate externalities. Moreover, this evolutionary stable preference leads to Walrasian behavior in those classes of games. |
| Keywords: | ambiguity, Knightian uncertainty, Choquet expected utility, neo-additive capacity, Hurwicz criterion, Maximin, Minimax, Ellsberg paradox, overconfidence, supermodularity, aggregative games, monotone comparative statics, playing the field, evolution of preferences |
| JEL: | C72 C73 D43 D81 L13 |
| Date: | 2005–11 |
| URL: | http://d.repec.org/n?u=RePEc:trf:wpaper:68&r=upt |
| By: | Mauro Boianovsky |
| Abstract: | The paper investigates Dennis Robertson's effort to defend the Cambridge utilitarian tradition against the so-called "new welfare economics" in the 1950s. Robertson's sustained and isolated endeavor to rescue Marshallian cardinal utility attracted the attention of economists at the time. According to Robertson, welfare economics should be based on cardinal utility, and the ordinalist revolution in the consumer and welfare theories should be rejected. It was only by sticking to the study of the economic or material aspects of welfare under the assumption of measurable utility that the economist would regain its ability to approach economic welfare as an objective of economic policy. |
| JEL: | B21 B31 |
| Date: | 2005 |
| URL: | http://d.repec.org/n?u=RePEc:anp:en2005:010&r=upt |
| By: | Rubens Penha Cysne |
| Abstract: | This paper uses 1992:1-2004:2 quarterly data and two diferent methods (approximation under lognormality and calibration) to evaluate the existence of an equity- premium puzzle in Brazil. In contrast with some previous works in the Brazilian literature, I conclude that the model used by Mehra and Prescott (1985), either with additive or recursive preferences, is not able to satisfactorily rationalize the equity premium observed in the Brazilian data. The second contribution of the paper is calling the attention to the fact that the utility function calculated under the discrete-state approximation may not exist if the data (as it is the case with Brazilian time series) implies the existence of states in which high negative rates of consumption growth are attained with relatively high probability. |
| JEL: | G12 E40 |
| Date: | 2005 |
| URL: | http://d.repec.org/n?u=RePEc:anp:en2005:088&r=upt |
| By: | Mohamed Anouar Razgallah (GATE CNRS) |
| Abstract: | Using a model of bivariate decision under risk, we analyse the health insurance demand when there are two sources of risk: a health risk and an uninsurable one. We examine how the uninsurable risk affects the coverage of the health risk. We show that the determinants of the demand for health insurance are not only the correlation between the health and uninsurable risks as shown by Doherty and Schlesinger (1983a) and the variation of the marginal utility of wealth with respect to the health status (Rey, 2003) but also the way in which the occurrence of the uninsurable risk affects the marginal utility of wealth. |
| Keywords: | Correlated risks, Health insurance, State-dependent utility |
| JEL: | D81 I11 I18 |
| Date: | 2005–11 |
| URL: | http://d.repec.org/n?u=RePEc:gat:wpaper:0504&r=upt |
| By: | Tam Bang Vu (Department of Economics, University of Hawaii at Manoa) |
| Abstract: | Mankiw (1982) shows that consumer durables expenditures should follow a linear ARMA(1,1) process, but the data analyzed supports an AR(1) process instead; thus, a puzzle. In this paper, we employ a more general utility function than Mankiw's quadratic one. Further, the disturbance and depreciation rate are respecified, respectively, as multiplicative and stochastic. The analytical consequence is a nonlinear ARMA(infinity,1) process, which implies that the linear ARMA(1,1) is a misspecification. A historical data analysis appears to support the nonlinear model. Since actual data are influenced by historical events, we also carry out a Monte Carlo study to strengthen our point. |
| Date: | 2005 |
| URL: | http://d.repec.org/n?u=RePEc:hai:wpaper:200515&r=upt |
| By: | Bezalel Peleg; Hans Peters |
| Abstract: | Effectivity functions for finitely many players and alternatives are considered. It is shown that every monotonic and superadditive effectivity function can be augmented with equal chance lotteries to a finite lottery model - i.e., an effectivity function that preserves the original effectivity in terms of supports of lotteries - which has a Nash consistent representation. In other words, there exists a finite game form which represents the lottery model and which has a Nash equilibrium for any profile of utility functions, where lotteries are evaluated by their expected utility. No additional condition on the original effectivity function is needed. |
| Date: | 2005–09 |
| URL: | http://d.repec.org/n?u=RePEc:huj:dispap:dp404&r=upt |
| By: | Ottone, Stefania; Ponzano, Ferruccio |
| Abstract: | The aim of this paper is to improve on the model by Fehr and Schmidt (1999) by developing a non-linear model (that leads to interior rather than corner solutions) and by taking into account that different levels of income imply different reactions of fair-minded people. We suggest to modify the inequity-aversion utility function proposed by Fehr and Schmidt by taking into account not only the difference between players' payoffs, but also their absolute value. This allows for a non-linear utility function where different stakes lead to different unique optimal interior solutions. |
| JEL: | A13 C72 C91 D63 D64 |
| Date: | 2005–11 |
| URL: | http://d.repec.org/n?u=RePEc:uca:ucapdv:51&r=upt |
| By: | Stefan Ankirchner |
| Abstract: | The utility maximisation problem is considered for investors with anticipative additional information. We distinguish between models with conditional measures and models with enlarged filtrations. The dual functions of the maximal expected utility are determined with the help of f-divergences. We assume that our measures are absolutely continuous with respect to a local martingale measure (LMM), but not necessarily equivalent. Thus we do not exclude arbitrage. |
| Keywords: | utility maximisation, additional information, enlargement of filtrations, conditional measures, convex conjugate function, dual function, f-divergence |
| JEL: | C61 D82 |
| Date: | 2005–05 |
| URL: | http://d.repec.org/n?u=RePEc:hum:wpaper:sfb649dp2005-029&r=upt |
| By: | Istvan Konya; Peter Benczur (Economics Magyar Nemzeti Bank) |
| Keywords: | real effects of nominal shocks, endogenous pass-through, two-sector growth model, q-theory, money-in-the-utility |
| JEL: | F32 F41 F43 |
| Date: | 2005 |
| URL: | http://d.repec.org/n?u=RePEc:red:sed005:51&r=upt |
| By: | Mariano Croce; Riccardo Colacito (Economics New York University) |
| Keywords: | Asset pricing, international finance, recursive utility |
| JEL: | G00 |
| Date: | 2005 |
| URL: | http://d.repec.org/n?u=RePEc:red:sed005:794&r=upt |
| By: | Morten Christensen (University of Southern Denmark); Eckhard Platen (School of Finance and Economics, University of Technology, Sydney) |
| Abstract: | We analyze portfolio strategies which are locally optimal, meaning that they maximize the Sharpe ratio in a general continuous time jump-di®usion framework. These portfolios are characterized explicitly and compared to utility based strategies. In the presence of jumps, maximizing the Sharpe ratio is shown to be generally inconsistent with maximizing expected utility, but this is shown to depend strongly on market completeness and whether event risk is priced. |
| Date: | 2005–11–01 |
| URL: | http://d.repec.org/n?u=RePEc:uts:rpaper:170&r=upt |