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図書

図書
Darrell Duffie
出版情報: Princeton, N.J. : Princeton University Press, c2001  xix, 465 p. ; 24 cm
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図書

図書
ダレル・ダフィー著 ; 本多俊毅訳
出版情報: 東京 : NTT出版, 2011.6  vi, 129p ; 22cm
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図書

図書
Darrell Duffie
出版情報: Boston ; San Diego ; Tokyo : Academic Press, c1988  xx, 358 p. ; 24 cm
シリーズ名: Economic theory, econometrics, and mathematical economics
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目次情報: 続きを見る
Preface
Introduction
Market Equilibrium / A.:
Equilibrium under Uncertainty / B.:
Security-Spot Market Equilibrium / C.:
State Pricing Model of Securities / D.:
Binomial Arbitrage Pricing Model of Securities / E.:
Capital Asset Pricing Model / F.:
Stochastic Control Pricing Model / G.:
The Potential-Price Matrix / H.:
Ito's Lemma--A Simple Case / I.:
Continuous-Time Portfolio Control / J.:
Black-Scholes Option Pricing Formula / K.:
Representative Agent Asset Pricing / L.:
Exercises
Notes
Static Economies / Chapter I.:
The Geometry of Choices and Prices / 1.:
Vector Spaces
Normed Spaces
Convexity and Cones
Function Spaces
Topology
Duality
Dual Representation
Preferences / 2.:
Preference Relations
Preference Continuity and Convexity
Utility Functions
Utility Representation
Quasi-Concave Utility
Monotonicity
Non-Satiation
Primitives of an Economy / 3.:
Equilibria
Exchange and Net Trade Economies
Production and Exchange Equilibria
Equilibrium and Efficiency
Efficiency and Equilibrium
Existence of Equilibria
First Probability Concepts / 4.:
Probability Spaces
Random Variables and Distributions
Measurability, Topology, and Partitions
Almost Sure Events and Versions
Expectation and Integration
Distribution and Density Functions
Expected Utility / 5.:
Von-Neumann-Morgenstern and Savage Models of Preferences
Expected Utility Representation
Preferences over Probability Distributions
Mixture Spaces and the Independence Axiom
Axioms for Expected Utility
Special Choice Spaces / 6.:
Banach Spaces
Measurable Function Spaces
L[superscript q] Spaces
L[superscript [infinity] Spaces
Riesz Representation
Continuity of Positive Linear Functionals
Hilbert Spaces
Portfolios / 7.:
Span and Vector Subspaces
Linearly Independent Bases
Equilibrium on a Subspace
Security Market Equilibria
Constrained Efficiency
Optimization Principles / 8.:
First Order Necessary Conditions
Saddle Point Theorem
Kuhn-Tucker Theorem
Superdifferentials and Maxima
Second Probability Concepts / 9.:
Changing Probabilities
Changing Information
Conditional Expectation
Properties of Conditional Expectation
Expectation in General Spaces
Jensen's Inequality
Independence and The Law of Large Numbers
Risk Aversion / 10.:
Defining Risk Aversion
Risk Aversion and Concave Expected Utility
Risk Aversion and Second Order Stochastic Dominance
Equilibrium in Static Markets Under Uncertainty / 11.:
Markets for Assets with a Variance
Beta Models: Mean-Covariance Pricing
The CAPM and APT Pricing Approaches
Variance Aversion
The Capital Asset Pricing Model
Proper Preferences
Stochastic Economies / Chapter II.:
Event Tree Economies / 12.:
Event Trees
Security and Spot Markets
Trading Strategies
Marketed Subspaces and Tight Markets
Dynamic and Static Equilibria
Dynamic Spanning and Complete Markets
A Security Valuation Operator
Dynamically Complete Markets Equilibria
Dynamically Incomplete Markets Equilibria
Generic Existence of Equilibria with Real Securities
Arbitrage Security Valuation and State Prices
A Dynamic Theory of the Firm / 13.:
Stock Market Equilibria
An Example
Security Trading by Firms
Invariance of Stock Values to Security Trading by Firms
Modigliani-Miller Theorem
Invariance of Firm's Total Market Value Process
Firms Issue and Retire Securities
Tautology of Complete Information Models
The Goal of the Firm
Stochastic Processes / 14.:
The Information Filtration
Informationally Adapted Processes
Information Generated by Processes and Event Trees
Technical Continuity Conditions
Martingales
Brownian Motion and Poisson Processes
Stopping Times, Local Martingales, and Semimartingales
Stochastic Integrals and Gains From Security Trade / 15.:
Discrete-Time Stochastic Integrals
Continuous-Time Primitives
Simple Continuous-Time Integration
The Stochastic Integral
General Stochastic Integrals
Martingale Multiplicity
Stochastic Integrals and Changes of Probability
Stochastic Equilibria / 16.:
Dynamic Spanning
Transformations to Martingale Gains from Trade / 17.:
Introduction: The Finite-Dimensional Case
Dividend and Price Processes
Self-Financing Trading Strategies
Representation of Implicit Market Values
Equivalent Martingale Measures
Choice of Numeraire
A Technicality
Generalization to Many Goods
Generalization to Consumption Through Time
Discrete-Time Asset Pricing / Chapter III.:
Markov Processes and Markov Asset Valuation / 18.:
Markov Chains
Transition Matrices
Metric and Borel Spaces
Conditional and Marginal Distributions
Markov Transition
Transition Operators
Chapman-Kolmogorov Equation
Sub-Markov Transition
Markov Arbitrage Valuation
Abstract Markov Process
Discrete-Time Markov Control / 19.:
Robinson Crusoe Example
Dynamic Programming with a Finite State Space
Borel-Markov Control Models
Existence of Stationary Markov Optimal Control
Measurable Selection of Maxima
Bellman Operator
Contraction Mapping and Fixed Points
Bellman Equation
Finite Horizon Markov Control
Stochastic Consumption and Investment Control
Discrete-Time Equilibrium Pricing / 20.:
Markov Exchange Economies
Optimal Portfolio and Consumption Policies
Conversion to a Borel-Markov Control Problem
Markov Equilibrium Security Prices
Relaxation of Short-Sales Constraints
Markov Production Economies
A Central Planning Stochastic Production Problem
Market Decentralization of a Growth Economy
Markov Stock Market Equilibrium
Continuous-Time Asset Pricing / Chapter IV.:
An Overview of the Ito Calculus / 21.:
Ito Processes and Integrals
Ito's Lemma
Stochastic Differential Equations
Feynman-Kac Formula
Girsanov's Theorem: Change of Probability and Drift
The Black-Scholes Model of Security Valuation / 22.:
Binomial Pricing Model
Black-Scholes Framework
Reduction to a Partial Differential Equation
The Black-Scholes Option Pricing Formula
An Application of the Feynman-Kac Formula
An Extension
Central Limit Theorems
Limiting Binomial Formula
Uniform Integrability
An Application of Donsker's Theorem
An Application of Girsanov's Theorem
An Introduction to the Control of Ito Processes / 23.:
Sketch of Bellman's Equation
Regularity Requirements
Formal Statement of Bellman's Equation
Portfolio Choice with I.I.D. Returns / 24.:
The Portfolio Control Problem
The Solution
Continuous-Time Equilibrium Asset Pricing / 25.:
The Setting
Definition of Equilibrium
Regularity Conditions
Equilibrium Theorem
Conversion to Consumption Numeraire
Equilibrium Interest Rates
The Consumption-Based Capital Asset Pricing Model
The Cox-Ingersoll-Ross Term Structure Model
Bibliography
Author Index
Symbol Glossary
Subject Index
Preface
Introduction
Market Equilibrium / A.:
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