David M. Kreps

Speculative Investor Behavior in a Stock Market with Heterogeneous Expectations

I. Introduction, 323.—II. Formulation, 325.—III. An example, 326.—IV. Consistent price schemes, 328.—V. Back to the example, 332.—VI. Relaxing the assumptions, 333.—VII. Concluding remarks, 334.

Arbitrage and equilibrium in economies with infinitely many commodities

Abstract An ‘arbitrage opportunity’ for a class of agents is a commodity bundle that will increase the utility of any of the agents and that has non-positive price. The non-existence of ‘arbitrage opportunities’ is necessary and sufficient for the existence of an economic equilibrium. A bundle is ‘priced by arbitrage’ if there is a unique price that it can command without causing an ‘arbitrage opportunity’ to exist. For economies that have infinitely many commodities, appropriate notions of ‘arbitrage opportunities’ and ‘bundles priced by arbitrage’ depend on the continuity of agents’ preferences. This paper develops these notions, thereby providing a foundation for recent work in financial theory concerning arbitrage in continuous-time models of securities markets.

A note on "fulfilled expectations" equilibria

In this note, the “fulfilled expectations” equilibrium notion, found in Green [3], Grossman [5], and Kihlstrom and Mirman [S], is used to analyze a simple model of a repeated futures market. (The model used is similar to one advanced by Stiglitz [ 111.) We are primarily interested in examining this equilibrium notion in the context of this simple model, and we find that it gives rise to a number of very interesting economic phenomena. The model is specified in Section 2. The market considered exists solely for insurance purposes: Speculators have random nonmarket income which may be statistically dependent on a price which will prevail in an upcoming spot market. By speculating in a futures market for the spot market commodity, they can hedge against adverse fluctuations in their nonmarket income. (Presumably, this takes place in a world without a complete set of contingent markets.) In Section 3, the “fulfilled expectations” equilibrium notion is advanced in the context of this model. Economic motivation for this notion is given. An economic difficulty is immediately encountered: Information originally possessed by no speculator may be transmitted by equilibrium prices. This is easily resolved, by restricting attention to prices which contain no more information than is possessed by all the speculators. However, when attention is so restricted, another problem is encountered: An equilibrium need not exist. An example of this is given in Section 4. Another difficulty with this equilibrium concept arises in connection with the standard notion of a demand correspondence. Roughly, a

Rational Learning and Rational Expectations

Much recent work in the economics of information has stemmed from the observation that demand functions, and therefore prices, reflect agents’ private information. Given an adequate understanding of the relationship between private information and equilibrium prices, it is possible to infer some or all of the private information. It seems natural to suppose, therefore, that agents will endeavour to use the information contained in equilibrium prices.

On the robustness of equilibrium refinements

The philosophy of equilibrium refinements is that the analyst, if he knows things about the structure of the game, can reject some Nash equilibria as unreasonable. The word “know†in the preceding sentence deserves special emphasis. If in a fixed game the analyst can reject a particular equilibrium outcome, but he cannot do so for games arbitrarily “close by,†then he may have second thoughts about rejecting the outcome. We consider several notions of distance between games, and we characterize their implications for the robustness of equilibrium refinements.

On intertemporal preferences in continuous time: The case of certainty☆

Abstract Different topologies on the space of certain consumption patterns in a continuous time setting are discussed. A family of topologies which give an economically reasonable sense of closeness and have an appropriate intertemporal flavor is suggested. The topological duals of our suggested topologies are essentially spaces of Lipschitz continuous functions. Any utility functional whose felicity function at any time t depends explicitly on the consumption at that time and is not linear in it is not continuous in any one of our topologies. A class of utility functionals that are continuous in the suggested topologies and that capture the intuitively appealing notion that consumptions at nearby dates are almost perfect substitutes is provided. We then give necessary and sufficient conditions for a consumption plan to be optimal for this class of utility functionals. We demonstrate our general theory by solving in closed form the optimal consumption problem for a particular utility function. The optimal solution consists of a (possible) initial ‘gulp’ of consumption, or an initial period of no consumption, followed by consumption at the rate that maintains a constant ratio of wealth to an index of past consumption experience.

Models in Managerial Accounting

ical trends in this area; to identify general deficiencies on how this research has been carried out; to point out trends and deficiencies in specific subsets of this domain of research; and to point out directions for future research that will help rectify the deficiencies. Quite assuredly, our process was subjective, and our observations, criticisms, plaudits, recommendations, and chastisements are all properly labeled as personal opinion.

Decision Problems with Expected Utility Criteria, II: Stationarity

The study of sequential decision problems with expected utility criteria is continued. Stationary problems are defined similarly to stationary problems with additive or separable utility, except that an additional requirement, stationarity of the preference structure, is imposed. The optimality of stationary and memoryless strategies is investigated for problems with upper and lower convergent utility or which are upper or lower transient. By example, the definition of stationarity is seen to be inadequate for generalizations of “average reward” criteria. Simplifications in the strategy iteration algorithm which result from stationarity are discussed.

Decision Problems with Expected Utility Critera, I: Upper and Lower Convergent Utility

A countable stage, countable state, finite action decision problem is considered where the objective is the maximization of the expectation of an arbitrary utility function defined on the sequence of states. Basic concepts are formulated, generalizing the standard notions of the optimality equations, conserving and unimprovable strategies, and strategy and value iteration. Analogues of positive, negative and convergent dynamic programming are analyzed.

ON THE OPTIMALITY OF STRUCTURED POLICIES IN COUNTABLE STAGE DECISION PROCESSES. II: POSITIVE AND NEGATIVE PROBLEMS*

The analysis of structured countable stage decision processes, initiated in Porteus [11], is continued. The standard models of positive and negative dynamic programming are given in this context, thus extending these results to criteria other than the usual expected sum of rewards, such as expected utility criteria, certain stochastic games, risk sensitive Markov decision processes, and maximin criteria.For positive problems, (what are called) unimprovable strategies are optimal and the optimal value sequence is the least solution of the optimality equations exceeding an obvious lower bound. For negative problems, conserving strategies are optimal, and if one strategy is a one-step improvement on another, then it nets a greater value. (This rules out cycling in the strategy iteration procedure.) Also, transfinite methods are used to prove that the optimal value sequence is the greatest solution of the optimality equations less than an obvious upper bound. We indicate how all these results can be extended ...