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84
Utility Representation of an Incomplete Preference Relation
, 2000
"... We consider the problem of representing a (possibly) incomplete preference relation by means of a vectorvalued utility function. Continuous and semicontinuous representation results are reported in the case of preference relations that are, in a sense, not “too incomplete.” These results generalize ..."
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Cited by 64 (6 self)
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We consider the problem of representing a (possibly) incomplete preference relation by means of a vectorvalued utility function. Continuous and semicontinuous representation results are reported in the case of preference relations that are, in a sense, not “too incomplete.” These results generalize some of the classical utility representation theorems of the theory of individual choice, and paves the way towards developing a consumer theory that realistically allows individuals to exhibit some “indecisiveness” on occasion.
Laws of Large Numbers for Dynamical Systems with Randomly Matched Individuals
 Journal of Economic Theory
, 1992
"... Biologists and economists have analyzed populations where each individual interacts with randomly selected individuals. The random matching generates a very complicated stochastic system. Consequently biologists and economists have approximated such a system with a deterministic system. The justitic ..."
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Cited by 49 (0 self)
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Biologists and economists have analyzed populations where each individual interacts with randomly selected individuals. The random matching generates a very complicated stochastic system. Consequently biologists and economists have approximated such a system with a deterministic system. The justitication for such an approximation is that the population is assumed to be very large and thus some law of large numbers must hold. This paper gives a characterization of random matching schemes for countably infinite populations. In particular this paper shows that there exists a random matching scheme such that the stochastic system and the deterministic system are the same. Journal of Economic Literature Classification
Ambiguity without a State Space
, 2003
"... Many decisions involve both imprecise probabilities and intractable states of the world. Objective expected utility assumes unambiguous probabilities; subjective expected utility assumes a completely specified state space. This paper analyzes a third domain of preference: sets of consequential lotte ..."
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Cited by 29 (2 self)
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Many decisions involve both imprecise probabilities and intractable states of the world. Objective expected utility assumes unambiguous probabilities; subjective expected utility assumes a completely specified state space. This paper analyzes a third domain of preference: sets of consequential lotteries. Using this domain, we develop a theory of Knightian ambiguity without explicitly invoking any state space. We characterize a representation that integrates a monotone transformation of first order expected utility with respect to a second order measure. The concavity of the transformation and the weighting of the measure capture ambiguity aversion. We propose a definition for comparative ambiguity aversion and uniquely characterize absolute ambiguity neutrality. Finally, we discuss applications of the theory: reinsurance, games, and a mean–variance–ambiguity portfolio frontier.
Optimal lifetime consumptionportfolio strategies under trading constraints and generalized recursive preferences
 STOCHASTIC PROCESSES AND THEIR APPLICATIONS
, 2003
"... ..."
On depth and deep points: a calculus
 Inst. Mathematical Statistics Bull
, 1998
"... Abstract. For a general definition of depth in data analysis a differentiallike calculus is constructed in which the location case (the framework of Tukey’s median) plays a fundamental role similar to that of linear functions in the mathematical analysis. As an application, a lower bound for maxima ..."
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Cited by 22 (2 self)
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Abstract. For a general definition of depth in data analysis a differentiallike calculus is constructed in which the location case (the framework of Tukey’s median) plays a fundamental role similar to that of linear functions in the mathematical analysis. As an application, a lower bound for maximal regression depth is proved in the general multidimensional case—as conjectured by Rousseeuw and Hubert, and others. This lower bound is demonstrated to have an impact on the breakdown point of the maximum depth estimator. 1. Introduction and
Knowledge Creation as a Square Dance on the Hilbert Cube ∗
, 2006
"... This paper presents a micromodel of knowledge creation through the interactions among a group of people. Our model incorporates two key aspects of the cooperative process of knowledge creation: (i) heterogeneity of people in their state of knowledge is essential for successful cooperation in the jo ..."
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Cited by 21 (5 self)
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This paper presents a micromodel of knowledge creation through the interactions among a group of people. Our model incorporates two key aspects of the cooperative process of knowledge creation: (i) heterogeneity of people in their state of knowledge is essential for successful cooperation in the joint creation of new ideas, while (ii) the very process of cooperative knowledge creation affects the heterogeneity of people through the accumulation of knowledge in common. The model features myopic agents in a pure externality model of interaction. Surprisingly, in the general case for a large set of initial conditions we find that the equilibrium process of knowledge creation converges to the most productive state, where the population splits into smaller groups of optimal size; close interaction takes place within each group only. This optimal size is larger as the heterogeneity of knowledge is more important in the knowledge production process. Equilibrium paths are found analytically, and they are a discontinuous function of initial heterogeneity. JEL
Optimality conditions for maximization of setvalued functions
 J. OPTIM. THEORY APPL
, 1988
"... The maximization with respect o a cone of a setvalued function into possibly infinite dimensions i defined, and necessary and sufficient optimality conditions are established. In particular, an analogue of the Fritz John necessary optimality conditions is proved using a notion of derivative defined ..."
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Cited by 17 (0 self)
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The maximization with respect o a cone of a setvalued function into possibly infinite dimensions i defined, and necessary and sufficient optimality conditions are established. In particular, an analogue of the Fritz John necessary optimality conditions is proved using a notion of derivative defined in terms of tangent cones.
Distributional properties of correspondences on Loeb spaces
 YENENG SUN Journal of Functional Analysis
, 1996
"... We present some regularity properties for the set of distributions induced by the measurable selections of a correspondence over a Loeb space, which include closedness, convexity, compactness, purification, and semicontinuity. We also note that all the properties reported in the main theorems are no ..."
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Cited by 13 (9 self)
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We present some regularity properties for the set of distributions induced by the measurable selections of a correspondence over a Loeb space, which include closedness, convexity, compactness, purification, and semicontinuity. We also note that all the properties reported in the main theorems are not satisfied by some correspondences on the unit Lebesgue interval. 1996 Academic Press, Inc. 1.
Strong rotundity and optimization
 SIAM Journal on Optimization
, 1994
"... Abstract. Standard techniques from the study of wellposedness show that if a fixed convex objective function is minimized in turn over a sequence of convex feasible regions converging Mosco to a limiting feasible region, then the optimal solutions converge in norm to the optimal solution of the lim ..."
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Cited by 11 (10 self)
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Abstract. Standard techniques from the study of wellposedness show that if a fixed convex objective function is minimized in turn over a sequence of convex feasible regions converging Mosco to a limiting feasible region, then the optimal solutions converge in norm to the optimal solution of the limiting problem. Certain conditions on the objective function are needed as is a constraint qualification. If, as may easily occur in practice, the constraint qualification fails, stronger set convergence is required, together with stronger analytic/geometric properties of the objective function: strict convexity (to ensure uniqueness), weakly compact level sets (to ensure existence and weak convergence), and the Kadec property (to deduce norm convergence). By analogy with the Lp norms, such properties are termed "strong rotundity. " A very simple characterization ofstrongly rotund integral functionals on L1 is presented that shows, for example, that the BoltzmannShannon entropy x log x is strongly rotund. Examples are discussed, and the existence of everywhere and denselydefined strongly rotund functions is investigated.
Second Order Multivalued Boundary Value Problems
, 1998
"... . In this paper we use the method of upper and lower solutions to study multivalued SturmLiouville and periodic boundary value problems, with Caratheodory orientor field. We prove two existence theorems. One when the orientor field F (t; x; y) is convexvalued and the other when F (t; x; y) is n ..."
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Cited by 10 (0 self)
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. In this paper we use the method of upper and lower solutions to study multivalued SturmLiouville and periodic boundary value problems, with Caratheodory orientor field. We prove two existence theorems. One when the orientor field F (t; x; y) is convexvalued and the other when F (t; x; y) is nonconvex valued. Finally we show that the "convex" problem has extremal solutions in the order interval determined by an upper and a lower solution. 1. Introduction The method of upper and lower solutions has been successfully applied to study the existence of multiple solutions for initial and boundary value problems of the first and second order. This method generates solutions of the problem, located in an order interval with the upper and lower solutions serving as bounds. Moreover, this method coupled with some monotonicity type hypotheses, leads to monotone iterative techniques which generate in a constructive way (amenable to numerical treatment) the extremal solutions within the ord...