/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

Convex Analysisの二,三の進展について

I. THE RECURSIVE APPROACH 1. Introduction 2. An Overview 2.1 A Deterministic Model of Optimal Growth 2.2 A Stochastic Model of Optimal Growth 2.3 Competitive Equilibrium Growth 2.4 Conclusions and Plans II. DETERMINISTIC MODELS 3. Mathematical Preliminaries 3.1 Metric Spaces and Normed Vector Spaces 3.2 The Contraction Mapping Theorem 3.3 The Theorem of the Maximum 4. Dynamic Programming under Certainty 4.1 The Principle of Optimality 4.2 Bounded Returns 4.3 Constant Returns to Scale 4.4 Unbounded Returns 4.5 Euler Equations 5. Applications of Dynamic Programming under Certainty 5.1 The One-Sector Model of Optimal Growth 5.2 A "Cake-Eating" Problem 5.3 Optimal Growth with Linear Utility 5.4 Growth with Technical Progress 5.5 A Tree-Cutting Problem 5.6 Learning by Doing 5.7 Human Capital Accumulation 5.8 Growth with Human Capital 5.9 Investment with Convex Costs 5.10 Investment with Constant Returns 5.11 Recursive Preferences 5.12 Theory of the Consumer with Recursive Preferences 5.13 A Pareto Problem with Recursive Preferences 5.14 An (s, S) Inventory Problem 5.15 The Inventory Problem in Continuous Time 5.16 A Seller with Unknown Demand 5.17 A Consumption-Savings Problem 6. Deterministic Dynamics 6.1 One-Dimensional Examples 6.2 Global Stability: Liapounov Functions 6.3 Linear Systems and Linear Approximations 6.4 Euler Equations 6.5 Applications III. STOCHASTIC MODELS 7. Measure Theory and Integration 7.1 Measurable Spaces 7.2 Measures 7.3 Measurable Functions 7.4 Integration 7.5 Product Spaces 7.6 The Monotone Class Lemma

Recursive methods in economic dynamics

/pdf/the-theory-of-industrial-organization-19bejph0ej.pdf

The Theory of Industrial Organization

We explore in this chapter questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties. This endeavor is really a study of diffusion processes. Loosely speaking, the term diffusion is attributed to a Markov process which has continuous sample paths and can be characterized in terms of its infinitesimal generator.

Stochastic Differential Equations

We survey here some recent studies concerning what we call mean-field models by analogy with Statistical Mechanics and Physics. More precisely, we present three examples of our mean-field approach to modelling in Economics and Finance (or other related subjects...). Roughly speaking, we are concerned with situations that involve a very large number of “rational players” with a limited information (or visibility) on the “game”. Each player chooses his optimal strategy in view of the global (or macroscopic) informations that are available to him and that result from the actions of all players. In the three examples we mention here, we derive a mean-field problem which consists in nonlinear differential equations. These equations are of a new type and our main goal here is to study them and establish their links with various fields of Analysis. We show in particular that these nonlinear problems are essentially well-posed problems i.e., have unique solutions. In addition, we give various limiting cases, examples and possible extensions. And we mention many open problems.

Mean Field Games

We compare a sealed-bid uniform-price auction (the Treasury's experimentalformat) with a sealedbid discriminatory auction (tbe Treasury'sformat beretofore), assuming the good is perfectly divisible. We show that the auction theory thatprompted the experiment, which assumes single-unit demands, does not adequately describe the bidding game for Treasury securities. Collusive strategies are self-enforcing in uniform-price divisible-good auctions. In these equilibria, the sellers expected revenue is lower than in equilibria of discriminatory auctions.

Auctions of Divisible Goods: On the Rationale for the Treasury Experiment

The continuous-time version of A. Kyle's (1985) model of asset pricing with asymmetric information is studied. It is shown that there is a unique equilibrium pricing rule within a certain class. This pricing rule is obtained in closed form for general distributions of the asset value. A particular example is a lognormal distribution, for which the equilibrium price process is a geometric Brownian motion. General trading strategies are allowed. In equilibrium, the informed agent, who is risk neutral, has many optima, but he does not correlate his trades locally with the noise trades nor does he submit discrete orders. Article published by Oxford University Press on behalf of the Society for Financial Studies in its journal, The Review of Financial Studies.

Insider Trading in Continuous Time

In an extension of the Kyle (1985) model of continuous insider trading, it is shown that asymmetric information can make it impossible to price options by arbitrage. Even when an option would appear to be redundant, its introduction into the market can cause the volatility of the underlying asset to become stochastic. This eliminates the potential for dynamically replicating the option. The change in the price process of the asset reflects a change in the information transmitted by volume and prices when the option is traded. Article published by Oxford University Press on behalf of the Society for Financial Studies in its journal, The Review of Financial Studies.

Asymmetric Information and Options

We analyze competition among informed traders in the continuous-time Kyle(1985) model, as Foster and Viswanathan (1996) do in discrete time. We explicitly describe the unique linear equilibrium when signals are imperfectly correlated and confirm the conjecture of Holden and Subrahmanyam (1992) that there is no linear equilibrium when signals are perfectly correlated. One result is that at some date, and at all dates thereafter, the market would have been more informationally efficient had there been a monopolist informed trader instead of competing traders. The relatively large amount of private information remaining near the end of trading causes the market to approach complete illiquidity. Copyright The American Finance Association 2000.

Kerry Back

Papers

Auctions of Divisible Goods: On the Rationale for the Treasury Experiment

Insider Trading in Continuous Time

Asymmetric Information and Options

Imperfect Competition among Informed Traders

Asset pricing for general processes