Modeling aggregate behavior and fluctuations in economics : stochastic views of interacting agents / Masanao Aoki.

Format:

Book

Author/Creator:

Aoki, Masanao, author.

Language:

English

Subjects (All):

Demand (Economic theory)--Mathematical models.

Demand (Economic theory).

Supply and demand--Mathematical models.

Supply and demand.

Consumption (Economics)--Mathematical models.

Consumption (Economics).

Business cycles--Mathematical models.

Business cycles.

Statics and dynamics (Social sciences)--Mathematical models.

Statics and dynamics (Social sciences).

Stochastic processes--Mathematical models.

Stochastic processes.

Physical Description:

1 online resource (xv, 263 pages) : digital, PDF file(s).

Edition:

1st ed.

Other Title:

Modeling Aggregate Behavior & Fluctuations in Economics

Place of Publication:

Cambridge : Cambridge University Press, 2002.

Language Note:

English

Summary:

This book has two components: stochastic dynamics and stochastic random combinatorial analysis. The first discusses evolving patterns of interactions of a large but finite number of agents of several types. Changes of agent types or their choices or decisions over time are formulated as jump Markov processes with suitably specified transition rates: optimisations by agents make these rates generally endogenous. Probabilistic equilibrium selection rules are also discussed, together with the distributions of relative sizes of the bases of attraction. As the number of agents approaches infinity, we recover deterministic macroeconomic relations of more conventional economic models. The second component analyses how agents form clusters of various sizes. This has applications for discussing sizes or shares of markets by various agents which involve some combinatorial analysis patterned after the population genetics literature. These are shown to be relevant to distributions of returns to assets, volatility of returns, and power laws.

Contents:

Our Objectives and Approaches

Partial List of Applications

States: Vectors of Fractions of Types and Partition Vectors

Vectors of Fractions

Partition Vectors

Jump Markov Processes

The Master Equation

Decomposable Random Combinatorial Structures

Sizes and Limit Behavior of Large Fractions

Setting Up Dynamic Models

Two Kinds of State Vectors

Empirical Distributions

Exchangeable Random Sequences

Partition Exchangeability

Transition Rates

Detailed-Balance Conditions and Stationary Distributions

Continuous-Time Dynamics

Power-Series Expansion

Aggregate Dynamics and Fokker-Planck Equation

Discrete-Time Dynamics

Introductory Simple and Simplified Models

A Two-Sector Model of Fluctuations

Closed Binary Choice Models

A Polya Distribution Model

Open Binary Models

Two Logistic Process Models

Model 1: The Aggregate Dynamics and Associated Fluctuations

Model 2: Nonlinear Exit Rate

A Nonstationary Polya Model

An Example: A Deterministic Analysis of Nonlinear Effects May Mislead!

Aggregate Dynamics and Fluctuations of Simple Models

Dynamics of Binary Choice Models

Dynamics for the Aggregate Variable

Potentials

Critical Points and Hazard Function

Multiplicity

An Aspect of Random Combinatorial Features

Evaluating Alternatives

Representation of Relative Merits of Alternatives

Value Functions

Extreme Distributions and Gibbs Distributions

Type I: Extreme Distribution.

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references (p. 245-252) and indexes.

ISBN:

1-107-12030-6

1-280-15912-X

0-511-11865-1

0-511-01878-9

0-511-15665-0

0-511-32934-2

0-511-51064-0

0-511-04599-9

OCLC:

437063058