nep-upt New Economics Papers
on Utility Models and Prospect Theory
Issue of 2008‒03‒08
twelve papers chosen by
Alexander Harin
Modern University for the Humanities

  1. Improving the Risk Concept: A Revision of Arrow-Pratt Theory in the Context of Controlled Dynamic Stochastic Environments By DAN PROTOPOPESCU
  2. Sustainable preferences via nondiscounted, hyperreal intergenerational welfare functions By Pivato, Marcus
  3. When is there state independence? By Brian, HILL
  4. An additively separable representation in the Savage framework By Brian, HILL
  5. Uncertainty, learning and growth By Galindev, Ragchaasuren
  6. Foundations of Intrinsic Habit Formation By Kareen Rozen
  7. Allocating Security Expenditures under Knightian Uncertainty: an Info-Gap Approach By Michael Ben-Gad; Yakov Ben-Haim; Dan Peled
  8. Isolation, Assurance and Rules : Can Rational Folly Supplant Foolish Rationality? By Peter J. Hammond
  9. On Financial Markets where only Buy-And-Hold Trading is Possible By Constantinos Kardaras; Eckhard Platen
  10. The effect of relative wealth concerns on the cross-section of stock returns By JUAN PEDRO GOMEZ
  11. The Impact of Heterogeneous Trading Rules on the Limit Order Book and Order Flows By Carl Chiarella; Giulia Iori; Josep Perello
  12. Doubts and equilibria By Antonio Cabrales; Jose Ramon Uriarte

    Abstract: In the literature on risk, one generally assume that uncertainty is uniformly distributed over the entire working horizon, when the absolute risk-aversion 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 risk-neutrality. This borderline case must be envisaged with prudence in a dynamic stochastic context. The traditional measures of risk-aversion 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 Arrow-Pratt measures (in the small) give ambiguous  
    Keywords: Controlled dynamic stochastic system, optimal trajectory, closed-loop strategy, feedback-and-forward information, rational decision-maker, dynamic learning, endogenous risk-aversion, adaptive risk management, optimal risk-aversion threshold, excessive risk-averse behavior, risk perception, changing risk behavior.
    JEL: C61 D78 D81 D83
    Date: 2007–12–15
  2. By: Pivato, Marcus
    Abstract: We define an intergenerational social welfare function Sigma from |R^|N (the set of all infinite-horizon utility streams) into *|R (the ordered field of hyperreal numbers). The function Sigma is continuous, linear, and increasing, and is well-defined 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; infinite-horizon; nondiscounted; sustainable; hyperreal; nonstandard real numbers; nonstandard analysis;
    JEL: D71 D90 Q01
    Date: 2008–03–05
  3. By: Brian, HILL
    Abstract: It has been noticed that whether a preference relation can be represented by state-independent utilities as opposed to state-dependent 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 state-dependent 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 state-independent 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; State-dependent utility; Monotonicity axiom
    JEL: C69 D81
    Date: 2007–11–22
  4. 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 “state-dependent 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 state-dependent utility representation theorems in the Savage framework.
    Keywords: Expected utility; additive representation; state-dependent utility; monotonicity
    JEL: D81
    Date: 2007–10–29
  5. 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 long-term growth and short-term 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
  6. 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 decision-maker 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 choice-theoretic 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 time-nonseparable 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, Time-nonseparable preferences, Compensation, Weaning, Compensated separability, Gains monotonicity, Endogenously generated auxiliary spaces
    JEL: C60 D11 D90
    Date: 2008–03
  7. By: Michael Ben-Gad (Department of Economics, City University, London); Yakov Ben-Haim (Faculty of Mechanical Engineering, Technion-Israel Institute of Technology); Dan Peled (Department of Economics, University of Haifa)
    Abstract: We apply the information gap approach to resource allocation under Knightian (non-probabilistic) 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{vis-a-vis} the likelihood of armed conflict and its outcomes, robust-satisficing 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: Info-gap; Knightian Uncertainty; Robustness; Defense
    Date: 2008–03
  8. 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 “quasi-magically” 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
  9. 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 buyand-hold strategies is considered. Minimal assumptions are made on the nature of the asset-price process ? in particular, the semimartingale property is not assumed. Via a natural assumption of limited opportunities for unlimited resulting wealth from trading, coined the No-Unbounded-Profit-with-Bounded-Risk (NUPBR) condition, we establish that asset-prices 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 buy-and-hold strategies, optimal utilities and wealth processes resulting from continuous trading can be approximated arbitrarily well.
    Keywords: numeraire portfolio; semimartingales; buy-and-hold strategies; unbounded profit with bounded risk; supermartingale deflators; utility maximization.
    Date: 2008–02–01
  10. 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 cross-section of stock returns, the model performs substantially better than the CAPM, and as well as the Fama-French three factor model.
    Keywords: Local risk, Negative risk premium, Relative wealth concerns
    Date: 2008–02
  11. 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 order-driven 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, namely-fundamentalist, 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
  12. By: Antonio Cabrales; Jose Ramon Uriarte
    Abstract: In real life strategic interactions decision-makers are likely to entertain doubts about the degree of optimality of their play. To capture this feature of real choice-making, 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 doubt-based selection dynamic systems. We introduce the concepts of Mixed Strategy Doubt Equilibria, Mixed Strategy Doubt-Full 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

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