Temporal resolution of uncertainty and dynamic choice theory
01 Jan 1978-Econometrica (Institute for Mathematical Studies in the Social Sciences, Stanford Univ.)-Vol. 46, Iss: 1, pp 185-200
TL;DR: In this paper, the authors consider dynamic choice behavior under conditions of uncertainty, with emphasis on the timing of the resolution of uncertainty and provide an axiomatic treatment of the dynamic choice problem which still permits tractable analysis.
Abstract: We consider dynamic choice behavior under conditions of uncertainty, with emphasis on the timing of the resolution of uncertainty. Choice behavior in which an individual distinguishes between lotteries based on the times at which their uncertainty resolves is axiomatized and represented, thus the result is choice behavior which cannot be represented by a single cardinal utility function on the vector of payoffs. Both descriptive and normative treatments of the problem are given and are shown to be equivalent. Various specializations are provided, including an extension of "separable" utility and representation by a single cardinal utility function. CONSIDER THE FOLLOWING idealization of a dynamic choice problem with uncertainty. At each in a finite, discrete sequence of times t = 0, 1, . . ., T, an individual must choose an action d,. His choice is constrained by what we temporarily call the state at time t, xt. Then some random event takes place, determining an immediate payoff zt to the individual and the next state xt+l. The probability distribution of the pair (zt, xt+l) is determined by the action dt. The standard approach in analyzing this problem, which we will call the payoff vector approach, assumes that the individual's choice behavior is representable as follows: He has a von Neumann-Morgenstern utility function U defined on the vector of payoffs (z0, z1, . . ., ZT). Each strategy (which is a contingent plan for choosing actions given states) induces a probability distribution on the vector of payoffs. So the individual's choice of action is that specified by any optimal strategy, any strategy which maximizes the expectation of utility among all strategies (assuming sufficient conditions so that an optimal strategy exists). This paper presents an axiomatic treatment of the dynamic choice problem which is more general than the payoff vector approach, but which still permits tractable analysis. The fundamental difference between our treatment and the payoff vector approach lies in our treatment of the temporal resolution of uncertainty: In our models, uncertainty is "dated" by the time of its resolution, and the individual regards uncertainties resolving at different times as being different. For example, consider a situation in which a fair coin is to be flipped. If it comes up heads, the payoff vector will be (zo, z1) = (5, 10); if it is tails, the vector will be (5, 0). Because z0 = 5 in either case, the coin flip can take place at either time 0 or time 1. It will not matter when the flip occurs to someone who has cardinal utility on the vector of payoffs. But an individual can obey our axioms and prefer either one to the other. One justification for our approach is the well known "timeless-temporal" or "joint time-risk" feature of some models (usually models which are not "complete"). For example, preferences on income streams which are induced from primitive preferences on consumption streams in general depend upon when the
Citations
More filters
TL;DR: In this paper, a class of recursive, but not necessarily expected utility, preferences over intertemporal consumption lotteries is developed, which allows risk attitudes to be disentangled from the degree of inter-temporal substitutability, leading to a model of asset returns in which appropriate versions of both the atemporal CAPM and the inter-time consumption-CAPM are nested as special cases.
Abstract: This paper develops a class of recursive, but not necessarily expected utility, preferences over intertemporal consumption lotteries An important feature of these general preferences is that they permit risk attitudes to be disentangled from the degree of intertemporal substitutability Moreover, in an infinite horizon, representative agent context these preference specifications lead to a model of asset returns in which appropriate versions of both the atemporal CAPM and the intertemporal consumption-CAPM are nested as special cases In our general model, systematic risk of an asset is determined by covariance with both the return to the market portfolio and consumption growth, while in each of the existing models only one of these factors plays a role This result is achieved despite the homotheticity of preferences and the separability of consumption and portfolio decisions Two other auxiliary analytical contributions which are of independent interest are the proofs of (i) the existence of recursive intertemporal utility functions, and (ii) the existence of optima to corresponding optimization problems In proving (i), it is necessary to define a suitable domain for utility functions This is achieved by extending the formulation of the space of temporal lotteries in Kreps and Porteus (1978) to an infinite horizon framework A final contribution is the integration into a temporal setting of a broad class of atemporal non-expected utility theories For homogeneous members of the class due to Chew (1985) and Dekel (1986), the corresponding intertemporal asset pricing model is derived
4,218 citations
Book•
24 Sep 2009
TL;DR: The authors dedicate this book to Julia, Benjamin, Daniel, Natan and Yael; to Tsonka, Konstatin and Marek; and to the Memory of Feliks, Maria, and Dentcho.
Abstract: List of notations Preface to the second edition Preface to the first edition 1. Stochastic programming models 2. Two-stage problems 3. Multistage problems 4. Optimization models with probabilistic constraints 5. Statistical inference 6. Risk averse optimization 7. Background material 8. Bibliographical remarks Bibliography Index.
2,443 citations
Cites background from "Temporal resolution of uncertainty ..."
...It is worth noting that time consistency of utility models was already discussed by Koopmans [135] and Kreps and Porteus [136, 137]....
[...]
TL;DR: In this article, the authors propose a model of preferences over acts such that the decision maker evaluates acts according to the expectation (over a set of probability measures) of an increasing transformation of an act's expected utility.
Abstract: We propose and axiomatize a model of preferences over acts such that the decision maker evaluates acts according to the expectation (over a set of probability measures) of an increasing transformation of an act's expected utility. This expectation is calculated using a subjective probability over the set of probability measures that the decision maker thinks are relevant given her subjective information. A key feature of our model is that it achieves a separation between ambiguity, identified as a characteristic of the decision maker's subjective information, and ambiguity attitude, a characteristic of the decision maker's tastes. We show that attitudes towards risk are characterized by the shape of the von Neumann-Morgenstern utility function, as usual, while attitudes towards ambiguity are characterized by the shape of the increasing transformation applied to expected utilities. We show that the negative exponential form of this transformation is the special case of constant ambiguity aversion. Ambiguity itself is defined behaviorally and is shown to be characterized by properties of the subjective set of measures. This characterization of ambiguity is formally related to the definitions of subjective ambiguity advanced by Epstein-Zhang (2001) and Ghirardato-Marinacci (2002). One advantage of this model is that the well-developed machinery for dealing with risk attitudes can be applied as well to ambiguity attitudes. The model is also distinct from many in the literature on ambiguity in that it allows smooth, rather than kinked, indifference curves. This leads to different behavior and improved tractability, while still sharing the main features (e.g., Ellsberg's Paradox, etc.). The Maxmin EU model (e.g., Gilboa and Schmeidler (1989)) with a given set of measures may be seen as an extreme case of our model with infinite ambiguity aversion. Two illustrative applications to portfolio choice are offered.
1,475 citations
TL;DR: In this article, the authors propose a theory of development that links the degree of market incompleteness to capital accumulation and growth, and show that the decentralized equilibrium is inefficient because individuals do not take into account their impact on others' diversification opportunities, and that the typical development pattern will consist of a lengthy period of primitive accumulation with highly variable output, followed by takeoff and financial deepening and, finally, steady growth.
Abstract: This paper offers a theory of development that links the degree of market incompleteness to capital accumulation and growth. At early stages of development, the presence projects limits the degree of risk spreading (diversification) that the economy can achieve. The desire to avoid highly risky investments slows down capital accumulation, and the inability to diversify idiosyncratic risk introduces a large amount of uncertainty in the growth process. The typical development pattern will consist of a lengthy period of “primitive accumulation” with highly variable output, followed by takeoff and financial deepening and, finally, steady growth. “Lucky” countries will spend relatively less time in the primitive accumulation stage and develop faster. Although all agents are price takers and there are no technological spillovers, the decentralized equilibrium is inefficient because individuals do not take into account their impact on others' diversification opportunities. We also show that our results generalize to economies with international capital flows.
1,438 citations
Book•
01 Jan 2001
TL;DR: In this article, the authors focus on richer applications of expected utility in finance, macroeconomics, and environmental economics, including the standard portfolio problem of choice under uncertainty involving two different assets, P the basic hyperplane separation theorem and log-supermodular functions as technical tools for solving various decision-making problems under uncertainty; s choice involving multiple risks; the Arrow-Debreu portfolio problem; consumption and saving; the equilibrium price of risk and time in an Arrow-debreu economy; and dynamic models of decision making.
Abstract: This book updates and advances the theory of expected utility as applied to risk analysis and financial decision making. Von Neumann and Morgenstern pioneered the use of expected utility theory in the 1940s, but most utility functions used in financial management are still relatively simplistic and assume a mean-variance world. Taking into account recent advances in the economics of risk and uncertainty, this book focuses on richer applications of expected utility in finance, macroeconomics, and environmental economics. The book covers these topics: expected utility theory and related concepts; the standard portfolio problem of choice under uncertainty involving two different assets; P the basic hyperplane separation theorem and log-supermodular functions as technical tools for solving various decision-making problems under uncertainty; s choice involving multiple risks; the Arrow-Debreu portfolio problem; consumption and saving; the equilibrium price of risk and time in an Arrow-Debreu economy; and dynamic models of decision making when a flow of information on future risks is expected over time. The book is appropriate for both students and professionals. Concepts are presented intuitively as well as formally, and the theory is balanced by empirical considerations. Each chapter concludes with a problem set.
1,416 citations
References
More filters
Book•
01 Jan 1967
TL;DR: The Borel subsets of a metric space Probability measures in the metric space and probability measures in a metric group Probability measure in locally compact abelian groups The Kolmogorov consistency theorem and conditional probability probabilistic probability measures on $C[0, 1]$ and $D[0-1]$ Bibliographical notes Bibliography List of symbols Author index Subject index as mentioned in this paper
Abstract: The Borel subsets of a metric space Probability measures in a metric space Probability measures in a metric group Probability measures in locally compact abelian groups The Kolmogorov consistency theorem and conditional probability Probability measures in a Hilbert space Probability measures on $C[0,1]$ and $D[0,1]$ Bibliographical notes Bibliography List of symbols Author index Subject index.
2,667 citations
Book•
01 Jan 1970
TL;DR: This book presents a concise yet mathematically complete treatment of modern utility theories that covers nonprobabilistic preference theory, the von Neumann-Morgenstern expected-utility theory and its extensions, and the joint axiomatization of utility and subjective probability.
Abstract: : The book presents a concise yet mathematically complete treatment of modern utility theories that covers nonprobabilistic preference theory, the von Neumann-Morgenstern expected-utility theory and its extensions, and the joint axiomatization of utility and subjective probability.
2,531 citations
TL;DR: In this paper, a utility theory for decision-making is proposed for decision making in the field of operational research, which is based on the concept of utility-theoretic decision making.
Abstract: (1971). Utility Theory for Decision Making. Journal of the Operational Research Society: Vol. 22, No. 3, pp. 308-309.
738 citations
TL;DR: In this article, the topology of the prospect space itself is removed, the previous axioms are weakened, an infinite number of sure prospects are allowed, and the existence of a measurable utility is established.
Abstract: : Previous treatments of this approach brought topological considerations of the prospects space into the axioms. In this paper considerations of the topology of the prospect space itself are removed, the previous axioms are weakened an infinite number of sure prospects are allowed. On the basis of these axioms the existence of a measurable utility is established.
687 citations
375 citations
"Temporal resolution of uncertainty ..." refers background in this paper
...Yaari [6]) is touched upon....
[...]
...Hammond [3] and Peleg and Yaari [6] , we...
[...]