Security Markets

Stochastic Models

By: Darrell Duffie (Editor)

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Hardcover | 28 July 1988

At a Glance

Hardcover
250 Pages

Dimensions(cm)
25.0 x 152.0 x 229.0

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$345.99

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This is a graduate level work covering the economic principles of security markets. Interested readers include students and researchers in economics and finance, as well as financial analysts following the latest theoretical developments in capital asset pricing.

Industry Reviews

"Contains extensive and very valuable references to both the mathematical and the financial economics literature. It will be (in fact, it already is) the main reference in the area of dynamic, competitive securities markets models with systematic information." --MATHEMATICAL REVIEWS "This is a high-level introduction to the theory of security markets, dealing principally with the allocational role and valuation of financial securities in a competitive setting. The intent is to provide a unified general equilibrium framework for such recent advances in finance as: the Sharpe-Litner Capital Asset Pricing Model and its discrete and continuous time analogues due to Lucas, Merton, and Breden the Black-Scholes Option Pricing Formula and its extensions into Martingale theory by Harrison and Kreps the continuous-time portfolio control models of Merton the term structure theory of Cox, Ingersoll, and Ross.

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Non-Fiction Accounting & Finance Finance Investment & Securities Economics Economic Theory & Philosophy Econometrics

Preface	p. xvii
Introduction	p. 1
Market Equilibrium	p. 1
Equilibrium under Uncertainty	p. 2
Security-Spot Market Equilibrium	p. 2
State Pricing Model of Securities	p. 5
Binomial Arbitrage Pricing Model of Securities	p. 6
Capital Asset Pricing Model	p. 10
Stochastic Control Pricing Model	p. 12
The Potential-Price Matrix	p. 15
Ito's Lemma--A Simple Case	p. 16
Continuous-Time Portfolio Control	p. 18
Black-Scholes Option Pricing Formula	p. 20
Representative Agent Asset Pricing	p. 22
Exercises	p. 24
Notes	p. 25
Static Economies	p. 27
The Geometry of Choices and Prices	p. 28
Vector Spaces	p. 28
Normed Spaces	p. 29
Convexity and Cones	p. 30
Function Spaces	p. 30
Topology	p. 30
Duality	p. 31
Dual Representation	p. 32
Exercises	p. 32
Notes	p. 35
Preferences	p. 35
Preference Relations	p. 35
Preference Continuity and Convexity	p. 35
Utility Functions	p. 35
Utility Representation	p. 36
Quasi-Concave Utility	p. 36
Monotonicity	p. 36
Non-Satiation	p. 37
Exercises	p. 37
Notes	p. 39
Market Equilibrium	p. 39
Primitives of an Economy	p. 39
Equilibria	p. 39
Exchange and Net Trade Economies	p. 40
Production and Exchange Equilibria	p. 41
Equilibrium and Efficiency	p. 42
Efficiency and Equilibrium	p. 42
Existence of Equilibria	p. 44
Exercises	p. 45
Notes	p. 49
First Probability Concepts	p. 50
Probability Spaces	p. 50
Random Variables and Distributions	p. 51
Measurability, Topology, and Partitions	p. 51
Almost Sure Events and Versions	p. 52
Expectation and Integration	p. 53
Distribution and Density Functions	p. 54
Exercises	p. 54
Notes	p. 55
Expected Utility	p. 56
Von-Neumann-Morgenstern and Savage Models of Preferences	p. 56
Expected Utility Representation	p. 56
Preferences over Probability Distributions	p. 57
Mixture Spaces and the Independence Axiom	p. 57
Axioms for Expected Utility	p. 59
Exercises	p. 60
Notes	p. 60
Special Choice Spaces	p. 61
Banach Spaces	p. 61
Measurable Function Spaces	p. 61
L[superscript q] Spaces	p. 61
L[superscript [infinity] Spaces	p. 62
Riesz Representation	p. 62
Continuity of Positive Linear Functionals	p. 63
Hilbert Spaces	p. 63
Exercises	p. 65
Notes	p. 67
Portfolios	p. 67
Span and Vector Subspaces	p. 67
Linearly Independent Bases	p. 68
Equilibrium on a Subspace	p. 68
Security Market Equilibria	p. 69
Constrained Efficiency	p. 70
Exercises	p. 70
Notes	p. 74
Optimization Principles	p. 74
First Order Necessary Conditions	p. 74
Saddle Point Theorem	p. 76
Kuhn-Tucker Theorem	p. 77
Superdifferentials and Maxima	p. 78
Exercises	p. 79
Notes	p. 81
Second Probability Concepts	p. 82
Changing Probabilities	p. 82
Changing Information	p. 83
Conditional Expectation	p. 83
Properties of Conditional Expectation	p. 84
Expectation in General Spaces	p. 85
Jensen's Inequality	p. 85
Independence and The Law of Large Numbers	p. 86
Exercises	p. 87
Notes	p. 89
Risk Aversion	p. 90
Defining Risk Aversion	p. 90
Risk Aversion and Concave Expected Utility	p. 90
Risk Aversion and Second Order Stochastic Dominance	p. 91
Exercises	p. 92
Notes	p. 92
Equilibrium in Static Markets Under Uncertainty	p. 93
Markets for Assets with a Variance	p. 93
Beta Models: Mean-Covariance Pricing	p. 93
The CAPM and APT Pricing Approaches	p. 94
Variance Aversion	p. 95
The Capital Asset Pricing Model	p. 95
Proper Preferences	p. 96
Existence of Equilibria	p. 98
Exercises	p. 99
Notes	p. 101
Stochastic Economies	p. 103
Event Tree Economies	p. 104
Event Trees	p. 104
Security and Spot Markets	p. 105
Trading Strategies	p. 107
Equilibria	p. 107
Marketed Subspaces and Tight Markets	p. 108
Dynamic and Static Equilibria	p. 109
Dynamic Spanning and Complete Markets	p. 109
A Security Valuation Operator	p. 111
Dynamically Complete Markets Equilibria	p. 111
Dynamically Incomplete Markets Equilibria	p. 113
Generic Existence of Equilibria with Real Securities	p. 113
Arbitrage Security Valuation and State Prices	p. 115
Exercises	p. 115
Notes	p. 116
A Dynamic Theory of the Firm	p. 118
Stock Market Equilibria	p. 118
An Example	p. 119
Security Trading by Firms	p. 121
Invariance of Stock Values to Security Trading by Firms	p. 123
Modigliani-Miller Theorem	p. 123
Invariance of Firm's Total Market Value Process	p. 124
Firms Issue and Retire Securities	p. 124
Tautology of Complete Information Models	p. 126
The Goal of the Firm	p. 127
Exercises	p. 128
Notes	p. 129
Stochastic Processes	p. 130
The Information Filtration	p. 130
Informationally Adapted Processes	p. 131
Information Generated by Processes and Event Trees	p. 133
Technical Continuity Conditions	p. 134
Martingales	p. 135
Brownian Motion and Poisson Processes	p. 135
Stopping Times, Local Martingales, and Semimartingales	p. 136
Exercises	p. 137
Notes	p. 138
Stochastic Integrals and Gains From Security Trade	p. 138
Discrete-Time Stochastic Integrals	p. 138
Continuous-Time Primitives	p. 140
Simple Continuous-Time Integration	p. 141
The Stochastic Integral	p. 142
General Stochastic Integrals	p. 144
Martingale Multiplicity	p. 146
Stochastic Integrals and Changes of Probability	p. 146
Exercises	p. 147
Notes	p. 147
Stochastic Equilibria	p. 148
Stochastic Economies	p. 148
Dynamic Spanning	p. 150
Existence of Equilibria	p. 151
Exercises	p. 154
Notes	p. 154
Transformations to Martingale Gains from Trade	p. 155
Introduction: The Finite-Dimensional Case	p. 155
Dividend and Price Processes	p. 156
Self-Financing Trading Strategies	p. 157
Representation of Implicit Market Values	p. 157
Equivalent Martingale Measures	p. 159
Choice of Numeraire	p. 162
A Technicality	p. 163
Generalization to Many Goods	p. 164
Generalization to Consumption Through Time	p. 165
Exercises	p. 166
Notes	p. 168
Discrete-Time Asset Pricing	p. 169
Markov Processes and Markov Asset Valuation	p. 170
Markov Chains	p. 170
Transition Matrices	p. 170
Metric and Borel Spaces	p. 171
Conditional and Marginal Distributions	p. 173
Markov Transition	p. 173
Transition Operators	p. 175
Chapman-Kolmogorov Equation	p. 175
Sub-Markov Transition	p. 176
Markov Arbitrage Valuation	p. 177
Abstract Markov Process	p. 179
Exercises	p. 179
Notes	p. 182
Discrete-Time Markov Control	p. 182
Robinson Crusoe Example	p. 183
Dynamic Programming with a Finite State Space	p. 184
Borel-Markov Control Models	p. 187
Existence of Stationary Markov Optimal Control	p. 189
Measurable Selection of Maxima	p. 190
Bellman Operator	p. 190
Contraction Mapping and Fixed Points	p. 191
Bellman Equation	p. 192
Finite Horizon Markov Control	p. 194
Stochastic Consumption and Investment Control	p. 195
Exercises	p. 199
Notes	p. 201
Discrete-Time Equilibrium Pricing	p. 202
Markov Exchange Economies	p. 202
Optimal Portfolio and Consumption Policies	p. 203
Conversion to a Borel-Markov Control Problem	p. 204
Markov Equilibrium Security Prices	p. 205
Relaxation of Short-Sales Constraints	p. 208
Markov Production Economies	p. 210
A Central Planning Stochastic Production Problem	p. 210
Market Decentralization of a Growth Economy	p. 211
Markov Stock Market Equilibrium	p. 213
Exercises	p. 214
Notes	p. 219
Continuous-Time Asset Pricing	p. 221
An Overview of the Ito Calculus	p. 222
Ito Processes and Integrals	p. 222
Ito's Lemma	p. 223
Stochastic Differential Equations	p. 224
Feynman-Kac Formula	p. 225
Girsanov's Theorem: Change of Probability and Drift	p. 228
Exercises	p. 230
Notes	p. 231
The Black-Scholes Model of Security Valuation	p. 232
Binomial Pricing Model	p. 233
Black-Scholes Framework	p. 235
Reduction to a Partial Differential Equation	p. 237
The Black-Scholes Option Pricing Formula	p. 239
An Application of the Feynman-Kac Formula	p. 239
An Extension	p. 240
Central Limit Theorems	p. 243
Limiting Binomial Formula	p. 245
Uniform Integrability	p. 247
An Application of Donsker's Theorem	p. 248
An Application of Girsanov's Theorem	p. 253
Exercises	p. 256
Notes	p. 264
An Introduction to the Control of Ito Processes	p. 266
Sketch of Bellman's Equation	p. 266
Regularity Requirements	p. 269
Formal Statement of Bellman's Equation	p. 269
Exercises	p. 271
Notes	p. 273
Portfolio Choice with I.I.D. Returns	p. 274
The Portfolio Control Problem	p. 274
The Solution	p. 276
Exercises	p. 279
Notes	p. 290
Continuous-Time Equilibrium Asset Pricing	p. 291
The Setting	p. 292
Definition of Equilibrium	p. 293
Regularity Conditions	p. 294
Equilibrium Theorem	p. 295
Conversion to Consumption Numeraire	p. 297
Equilibrium Interest Rates	p. 298
The Consumption-Based Capital Asset Pricing Model	p. 299
The Cox-Ingersoll-Ross Term Structure Model	p. 301
Exercises	p. 303
Notes	p. 320
Bibliography	p. 323
Author Index	p. 345
Symbol Glossary	p. 349
Subject Index	p. 351
Table of Contents provided by Syndetics. All Rights Reserved.

Security Markets

Stochastic Models

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

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