General Equilibrium Foundations of Finance: Structure of Incomplete Markets Models

Framsida
Springer Science & Business Media, 2002 - 299 sidor
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The purpose of this book is to give a sound economic foundation of finance. Finance is a coherent branch of applied economics that is designed to understand financial markets in order to give advice for practical financial decisions. This book argues that for a sound economic foundation of finance the famous general equilibrium model which in its modern form emphasizes the incompleteness of financial markets is well suited. The aim of the book is to demonstrate that financial markets can be meaningfully embedded into a more general system of markets including, for example, commodity markets. The interaction of these markets can be described via the well known notion of a competitive equilibrium. We argue that for a sound foundation this competitive equilibrium should be unique. In a first step we demonstrate that this essential goal cannot of be achieved based only on the rationality principle, i. e. on the assumption utility maximization of some utility function subject to the budget constraint. In particular we show that this important lack of structure is disturbing as well for the case of mean-variance utility functions which are the basis of the Capital Asset Pricing Model, one of the cornerstones of finance. The final goal of our book is to give reasonable restrictions on the agents' utility functions which lead to a well determined financial markets model.
 

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Innehåll

THE MODEL AND SOME FUNDAMENTALS
3
2 Consumer Characteristics
4
21 Expected Utility Hypothesis
8
3 Market Structure
12
32 Budget Set
13
4 Competitive Equilibria and NoArbitage
14
42 NoArbitrage Condition
16
43 Walras Law in the First Period
17
42 Explicit Pricing Formulas
124
43 Quasihomothetic Utility Functions
131
44 Quasilinear Utility Functions
139
45 The Theorem of MitjushinPolterovich
144
46 Gross Substitution in the Case of Small Relative Risk Aversion
158
47 Two Securities and Small Relative Risk Aversion
167
48 Overview of Conditions for Uniqueness in the Finance GEIModel
174
5 Robustness of the Number of Competitive Equilibria against Perturbations of the Asset Structure
176

44 Fundamental Theorem of Asset Pricing
18
45 Asset Pricing Theories
23
46 NoArbitrage Equilibrium Concept
24
5 Dual concepts of excess demand
28
6 Pricing of Derivatives
29
7 Efficiency of GEIequilibria
35
EXISTENCE OF EQUILIBRIA
39
1 Assumptions to obtain Existence
40
2 Discussion of the Assumptions
44
22 Boundary Behavior Assumption
49
23 A Final Remark
53
3 Properties of Excess Demand and Existence of Equilibria
54
STRUCTURE OF GEIEXCESS DEMAND
61
2 Mantels Theorem in Complete Markets
62
4 Anything Goes
63
5 Debreus Theorem
67
THE INDEXTHEOREM
71
2 Differentiability of Excess Demand
72
3 Equivalent Inward Pointing Vector Field
74
4 Local Uniqueness and the Index Theorem
75
UNIQUENESS OF COMPETITIVE EQUILIBRIA IN THE ARROWDEBREU MODEL
79
2 Defining Uniqueness of ArrowDebreu Equilibria
80
3 Useful Properties of Market Excess Demand
81
4 How to Obtain Uniqueness
83
41 Explicit Pricing Formulas
84
42 Existence of a Representative Consumer
94
43 How to Obtain Monotonicity
95
44 How to Obtain the Property of Gross Substitution
97
5 Overview of Conditions for Uniqueness in the ArrowDebreu Model
98
UNIQUENESS OF COMPETITIVE EQUILIBRIA IN THE FINANCE GEIMODEL
101
2 Defining Uniqueness of Financial Markets Equilibria
102
3 Properties of Market Demand for Assets
104
32 WARP and Monotonicity
108
33 Gross Substitution
113
34 Negative Definiteness versus Gross Substitution
121
4 How to Obtain Uniqueness
123
51 Further Properties of the Set of ArbitrageFree Prices
177
52 Continuous Differentiability of Asset Demand
186
53 Robustness of the Number of Equilibria
188
6 Limits of Transferability
192
61 Limits with QuasiLinearity
193
62 Limits with CobbDouglas Utility
196
63 Limited Risk Sharing
199
7 Uniqueness of Equilibria with Small Trading Volume
203
71 A Leading Example
204
72 Generalization of the Leading Example
206
APPENDIX 6A
208
2 Proof of Lemma 67
209
3 Proof of Lemma 68
210
THE CAPITAL ASSET PRICING MODEL
213
THE MODEL AND SOME FUNDAMENTALS
215
2 Information Structure And Commodity Space
216
3 The Agents Decision Problem
217
4 MeanVariance Utility an Alternative to Expected Utility
219
5 Equilibria in the CAPM without a Riskless Asset
221
6 Equilibria in the CAPM with a Riskless Asset
226
8 Monotonicity and Positive State Prices
228
EXISTENCE OF EQUILIBRIA
235
2 Necessary Conditions for Existence
237
3 Sufficient Conditions for Existence
238
4 Efficient Frontier
242
MARKET DEMAND FUNCTIONS IN THE CAPM
245
2 Structure of Market Demand
246
3 Number of CAPMequilibria
254
UNIQUENESS OF EQUILIBRIA IN THE CAPM
259
2 Uniqueness of equilibria in the CAPM with a riskless asset
261
3 Multiplicity of equilibria in the CAPM without a riskless asset
268
Mathematics
271
Assumptions
275
Main Results
279
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Sidan 287 - Thomas E. Copeland and J. Fred Weston, Financial Theory and Corporate Policy 198-199 (3d ed.
Sidan 288 - Mathematicians, Vancouver, 1974, 65-77. — , "The Rate of Convergence of the Core of an Economy/' J. Math. Econ., 1975, 2, 1-7. E. Dierker, "Two Remarks on the Number of Equilibria of an Economy," Econometrica, 1972, 40, 951-53. — — — , Topological Methods in Walrasian Economics, Lecture Notes in Economics and Mathematical Systems, 92, Berlin 1974. and H. Dierker, "The Local Uniqueness of Equilibria," Econometrica, 1972, 40, 867-81.

Om författaren (2002)

Thorsten Hens, Ph.D. University of Bonn, is professor for financial economics at the institute for empirical research in economics at the University of Zurich. He has held positions in Bielefeld, Paris and Stanford and is currently also an adjunct professor at the Finance Department of the Norwegian Business School, NHH, in Bergen. Beate Pilgrim, Ph.D. University of Bielefeld, is currently working for Reuters AG, Frankfurt.

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