
on Utility Models and Prospect Theory 
By:  DAN PROTOPOPESCU 
Abstract:  In the literature on risk, one generally assume that uncertainty is uniformly distributed over the entire working horizon, when the absolute riskaversion index is negative and constant. From this perspective, the risk is totally exogenous, and thus independent of endogenous risks. The classic procedure is "myopic" with regard to potential changes in the future behavior of the agent due to inherent random fluctuations of the system. The agent's attitude to risk is rigid. Although often criticized, the most widely used hypothesis for the analysis of economic behavior is riskneutrality. This borderline case must be envisaged with prudence in a dynamic stochastic context. The traditional measures of riskaversion are generally too weak for making comparisons between risky situations, given the dynamic complexity of the environment. This can be highlighted in concrete problems in finance and insurance, context for which the ArrowPratt measures (in the small) give ambiguous 
Keywords:  Controlled dynamic stochastic system, optimal trajectory, closedloop strategy, feedbackandforward information, rational decisionmaker, dynamic learning, endogenous riskaversion, adaptive risk management, optimal riskaversion threshold, excessive riskaverse behavior, risk perception, changing risk behavior. 
JEL:  C61 D78 D81 D83 
Date:  2007–12–15 
URL:  http://d.repec.org/n?u=RePEc:aub:autbar:727.08&r=upt 
By:  Pivato, Marcus 
Abstract:  We define an intergenerational social welfare function Sigma from R^N (the set of all infinitehorizon utility streams) into *R (the ordered field of hyperreal numbers). The function Sigma is continuous, linear, and increasing, and is welldefined even on unbounded (e.g. exponentially increasing) utility streams. This yields a complete social welfare ordering on R^N which is Pareto and treats all generations equally (i.e. does not discount future utility). In particular, it is what Chichilnisky (1996) calls a `sustainable' preference ordering: it is neither a `dictatorship of the present' nor a `dictatorship of the future'. We then show how an agent with no `pure' time preferences may still `informationally discount' the future, due to uncertainty. Last, we model intergenerational choice for an exponentially growing economy and population. In one parameter regime, our model shows `instrumental discounting' due to declining marginal utility of wealth. In another regime, we see a disturbing `Paradox of Eternal Deferral'. 
Keywords:  intergenerational choice; intertemporal choice; infinitehorizon; nondiscounted; sustainable; hyperreal; nonstandard real numbers; nonstandard analysis; 
JEL:  D71 D90 Q01 
Date:  2008–03–05 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:7461&r=upt 
By:  Brian, HILL 
Abstract:  It has been noticed that whether a preference relation can be represented by stateindependent utilities as opposed to statedependent utilities may depend on which acts count as constant acts [Schervish et al., 1990]. Indeed, this remark underlies an extension of Savage’s expected utility theory to the statedependent case that was proposed by Edi Karni [Karni, 1993]. This paper contains a characterisation of the preference relations that permit a choice of acts which can play the role of constant acts, and relative to which there is a representation involving a stateindependent utility function. This result applies both in the Savage and in the Anscombe & Aumann frameworks. It has as an immediate corollary an extension of Karni’s representation theorem. Finally, it is of methodological interest, insofar that it harnesses techniques from mathematical logic to prove a theorem of interest to decision theorists and economists. 
Keywords:  Subjective expected utility; Statedependent utility; Monotonicity axiom 
JEL:  C69 D81 
Date:  2007–11–22 
URL:  http://d.repec.org/n?u=RePEc:ebg:heccah:0883&r=upt 
By:  Brian, HILL 
Abstract:  This paper elicits an additively separable representation of preferences in the Savage framework (where the objects of choice are acts: measurable functions from an infinite set of states to a potentially finite set of consequences). A preference relation over acts is represented by the integral over the subset of the product of the state space and the consequence space which corresponds to the act, where this integral is calculated with respect to a “statedependent utility” measure on this space. The result applies at the stage prior to the separation of probabilities and utilities, and requires neither Savage’s P3 (monotonicity) nor his P4 (likelihood ordering). It may thus prove useful for the development of statedependent utility representation theorems in the Savage framework. 
Keywords:  Expected utility; additive representation; statedependent utility; monotonicity 
JEL:  D81 
Date:  2007–10–29 
URL:  http://d.repec.org/n?u=RePEc:ebg:heccah:0882&r=upt 
By:  Galindev, Ragchaasuren 
Abstract:  The paper extends Blackburn and Galindev (2003)' s stochastic growth model in which productivity growth entails both external and internal learning behaviour with a Constant Relative Risk Aversion utility function and productivity shocks. Consequently, the relationship between longterm growth and shortterm volatility depends not only on the relative importance of each learning mechanism but also on a parameter measuring individuals' attitude towards risk. 
Keywords:  Growth; Uncertainty; Learning 
JEL:  E32 O40 
Date:  2007–07 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:7398&r=upt 
By:  Kareen Rozen (Cowles Foundation, Yale University) 
Abstract:  We provide theoretical foundations for several common (nested) representations of intrinsic linear habit formation. These representations are dynamically consistent and additive, with geometrically decaying coefficients of habit formation. Our axiomatization introduces a revealed preference theory of weaning a decisionmaker from her habits using the device of compensation. We characterize linear habit formation in terms of the ability to wean using uniquely determined compensating streams. Moreover, we distinguish between habits that are responsive to weaning and those that are persistent, develop a simple choicetheoretic measure of the rate of habit decay, and demonstrate how to recover the entire sequence of habit formation coefficients from observed choice behavior. We introduce novel monotonicity and separability axioms that are appropriate for timenonseparable preferences. Our analysis suggests techniques for eliciting dynamic reference points from choice behavior and obtaining discounted utility representations on endogenously generated auxiliary spaces. 
Keywords:  Linear habit formation, Timenonseparable preferences, Compensation, Weaning, Compensated separability, Gains monotonicity, Endogenously generated auxiliary spaces 
JEL:  C60 D11 D90 
Date:  2008–03 
URL:  http://d.repec.org/n?u=RePEc:cwl:cwldpp:1642&r=upt 
By:  Michael BenGad (Department of Economics, City University, London); Yakov BenHaim (Faculty of Mechanical Engineering, TechnionIsrael Institute of Technology); Dan Peled (Department of Economics, University of Haifa) 
Abstract:  We apply the information gap approach to resource allocation under Knightian (nonprobabilistic) uncertainty in order to study how best to allocate public resources between competing defense measures. We demonstrate that when determining the level and composition of defense spending in an environment of extreme uncertainty \textit{visavis} the likelihood of armed conflict and its outcomes, robustsatisficing expected utility will usually be preferable to expected utility maximization. Moreover, our analysis suggests that in environments with unreliable information about threats to national security and their consequences, a desire for robustness to model misspecification in the decision making process will imply greater expenditure on certain types of defense measures at the expense of others. Our results also provide a positivist explanation of how governments seem to allocate security expenditures in practice. 
Keywords:  Infogap; Knightian Uncertainty; Robustness; Defense 
Date:  2008–03 
URL:  http://d.repec.org/n?u=RePEc:cty:dpaper:0805&r=upt 
By:  Peter J. Hammond (Department of Economics, University of Warwick) 
Abstract:  Consider an “isolation paradox” game with many identical players. By definition, conforming to a rule which maximizes average utility is individually a strictly dominated strategy. Suppose, however, that some players think “quasimagically” in accordance with evidential (but not causal) decision theory. That is, they act as if others’ disposition to conform, or not, is affected by their own behavior, even though they do not actually believe there is a causal link. Standard game theory excludes this. Yet such “rational folly” can sustain “rule utilitarian” cooperative behavior. Comparisons are made with Newcomb’s problem, and with related attempts to resolve prisoner’s dilemma. 
Date:  2008 
URL:  http://d.repec.org/n?u=RePEc:wrk:warwec:842&r=upt 
By:  Constantinos Kardaras; Eckhard Platen (School of Finance and Economics, University of Technology, Sydney) 
Abstract:  A financial market model where agents can only trade using realistic buyandhold strategies is considered. Minimal assumptions are made on the nature of the assetprice process ? in particular, the semimartingale property is not assumed. Via a natural assumption of limited opportunities for unlimited resulting wealth from trading, coined the NoUnboundedProfitwithBoundedRisk (NUPBR) condition, we establish that assetprices have to be semimartingales, as well as a weakened version of the Fundamental Theorem of Asset Pricing that involves supermartingale deflators rather than Equivalent Martingale Measures. Further, the utility maximization problem is considered and it is shown that using only buyandhold strategies, optimal utilities and wealth processes resulting from continuous trading can be approximated arbitrarily well. 
Keywords:  numeraire portfolio; semimartingales; buyandhold strategies; unbounded profit with bounded risk; supermartingale deflators; utility maximization. 
Date:  2008–02–01 
URL:  http://d.repec.org/n?u=RePEc:uts:rpaper:213&r=upt 
By:  JUAN PEDRO GOMEZ (Instituto de Empresa) 
Abstract:  There are several economic reasons why investors might want to hedge local risk resulting from relative wealth concerns; namely, keeping up with the Joneses preferences and competition for local assets in short supply. In equilibrium, hedging for these purposes results in a negative risk Premium for the local risk factors. We study the empirical implications of this equilibrium at the level of the nine US census divisions. As a proxy for the local risk factor we use regional labor income growth. In explaining the crosssection of stock returns, the model performs substantially better than the CAPM, and as well as the FamaFrench three factor model. 
Keywords:  Local risk, Negative risk premium, Relative wealth concerns 
Date:  2008–02 
URL:  http://d.repec.org/n?u=RePEc:emp:wpaper:wp0812&r=upt 
By:  Carl Chiarella (School of Finance and Economics University of Technology, Sydney); Giulia Iori (Department of Economics, City University, London); Josep Perello (Departament de Fisica Fonamental, Universitat de Barcelona) 
Abstract:  In this paper we develop a model of an orderdriven market where traders set bids and asks and post market or limit orders according to exogenously fixed rules. Agents are assumed to have three components to the expectation of future asset returns, namelyfundamentalist, chartist and noise trader. Furthermore agents differ in the characteristics describing these components, such as time horizon, risk aversion and the weights given to the various components. The model developed here extends a great deal of earlier literature in that the order submissions of agents are determined by utility maximisation, rather than the mechanical unit order size that is commonly assumed. In this way the order flow is better related to the ongoing evolution of the market. For the given market structure we analyze the impact of the three components of the trading strategies on the statistical properties of prices and order flows and observe that it is the chartist strategy that is mainly responsible of the fat tails and clustering in the artificial price data generated by the model. The paper provides further evidence that large price changes are likely to be generated by the presence of large gaps in the book. 
Keywords:  Market microstructure, limit orders, fundamentalism, chartism, large fluctuations. 
Date:  2008–03 
URL:  http://d.repec.org/n?u=RePEc:cty:dpaper:0804&r=upt 
By:  Antonio Cabrales; Jose Ramon Uriarte 
Abstract:  In real life strategic interactions decisionmakers are likely to entertain doubts about the degree of optimality of their play. To capture this feature of real choicemaking, we present here a model based on the doubts felt by an agent about how well is playing a game. The doubts are coupled with (and mutually reinforced by) imperfect discrimination capacity, which we model here by means of similarity relations. We assume that each agent builds procedural preferences defined on the space of expected payoffsstrategy frequencies attached to his current strategy. These preferences, together with an adaptive learning process lead to doubtbased selection dynamic systems. We introduce the concepts of Mixed Strategy Doubt Equilibria, Mixed Strategy DoubtFull Equilibria and Mixed Strategy Doubtless Equilibria and show the theoretical and the empirical relevance of these concepts 
Keywords:  Doubts, Bounded rationality, Evolutionary dynamics, Decision theory 
JEL:  C72 C73 D81 
Date:  2008–02 
URL:  http://d.repec.org/n?u=RePEc:cte:werepe:we080905&r=upt 