General equilibrium foundations of finance : structure of incomplete markets models / by Thorsten Hens and Beate Pilgrim.

Format:

Book

Author/Creator:

Hens, Thorsten.

Contributor:

Pilgrim, Beate.

Series:

Theory and decision library. Game theory, mathematical programming, and operations research ; Series C, v. 33.

Theory and decision library. Series C, Game theory, mathematical programming, and operations research ; v. 33

Language:

English

Subjects (All):

Finance--Mathematical models.

Capital market--Mathematical models.

Equilibrium (Economics).

Physical Description:

xxvii, 299 pages ; 24 cm.

Place of Publication:

Boston : Kluwer Academic Publishers, [2002]

Summary:

The purpose of General Equilibrium Foundations of Finance is to give a sound economic foundation of finance based on the general equilibrium model with incomplete markets which embodies the famous CAPM as an important special case. This goal is achieved by giving reasonable restrictions on the agents' characteristics that lead to a well determined financial markets model having a unique competitive equilibrium. The innovation of this book is to transfer and to extend the theoretical results on the structure of competitive equilibria into the modern context of incomplete financial markets. General Equilibrium Foundations of Finance should be easily accessible by advanced Ph.D. students as well as by theorists of any subfield of mathematical economics. It should be interesting both for theorists who are looking for possible applications of rigorous theorizing as well as for practitioners who seek for a theoretical foundation of fruitful applications of financial markets' models.

Contents:

Part I The General Equilibrium Model with Incomplete Markets

1. The Model and Some Fundamentals 3

1 Information Structure And Commodity Space 3

2 Consumer Characteristics 4

2.1 Expected Utility Hypothesis 8

3 Market Structure 12

3.1 Payoff Matrix 12

3.2 Budget Set 13

4 Competitive Equilibria and No-Arbitage 14

4.1 Financial Markets Equilibrium Concept 14

4.2 No-Arbitrage Condition 16

4.3 Walras Law in the First Period 17

4.4 Fundamental Theorem of Asset Pricing 18

4.5 Asset Pricing Theories 23

4.6 No-Arbitrage Equilibrium Concept 24

5 Dual concepts of excess demand 28

6 Pricing of Derivatives 29

7 Efficiency of GEI-equilibria 35

2. Existence of Equilibria 39

1 Assumptions to obtain Existence 40

2 Discussion of the Assumptions 44

2.1 Cheaper Point Assumption 44

2.2 Boundary Behavior Assumption 49

2.3 A Final Remark 53

3 Properties of Excess Demand and Existence of Equilibria 54

3. Structure of GEI-Excess Demand 61

1 The Intrinsic Limits of the Rationality Hypothesis 61

2 Mantel's Theorem in Complete Markets 62

4 Anything Goes 63

5 Debreu's Theorem 67

4. The Index-Theorem 71

1 The Idea of the Index Theorem 71

2 Differentiability of Excess Demand 72

3 Equivalent Inward Pointing Vector Field 74

4 Local Uniqueness and the Index Theorem 75

5. Uniqueness in the Arrow-Debreu Model 79

2 Defining Uniqueness of Arrow-Debreu Equilibria 80

3 Useful Properties of Market Excess Demand 81

4 How to Obtain Uniqueness 83

4.1 Explicit Pricing Formulas 84

4.2 Existence of a Representative Consumer 94

4.3 How to Obtain Monotonicity 95

4.4 How to Obtain the Property of Gross Substitution 97

5 Overview for the Arrow-Debreu Model 98

6. Uniqueness in the Finance GEI-Model 101

2 Defining Uniqueness of Financial Markets Equilibria 102

3 Properties of Market Demand for Assets 104

3.1 Decomposition of the Jacobian-Matrix 104

3.2 WARP and Monotonicity 108

3.3 Gross Substitution 113

3.4 Negative Definiteness versus Gross Substitution 121

4 How to Obtain Uniqueness 123

4.2 Explicit Pricing Formulas 124

4.3 Quasi-homothetic Utility Functions 131

4.4 Quasi-linear Utility Functions 139

4.5 The Theorem of Mitjushin-Polterovich 144

4.6 Small Risk Aversion 158

4.7 Two Securities and Small Relative Risk Aversion 167

4.8 Overview for the GEI-Model 174

5 Robustness of the Number of Equilibria 176

5.1 Further Properties of Arbitrage-Free Prices 177

5.2 Continuous Differentiability of Asset Demand 186

5.3 Robustness of the Number of Equilibria 188

6 Limits of Transferability 192

6.1 Limits with Quasi-Linearity 193

6.2 Limits with Cobb-Douglas Utility 196

6.3 Limited Risk Sharing 199

7 Uniqueness of Equilibria with Small Trading Volume 203

7.1 A Leading Example 204

7.2 Generalization of the Leading Example 206

1 Proof of Lemma 6.6 208

2 Proof of Lemma 6.7 209

3 Proof of Lemma 6.8 210

Part II The Capital Asset Pricing Model

7. The Model and Some Fundamentals 215

2 Information Structure And Commodity Space 216

3 The Agents' Decision Problem 217

4 Mean-Variance 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

7 Risk Aversion in the CAPM 226

8 Monotonicity and Positive State Prices 228

8. Existence of Equilibria 235

2 Necessary Conditions for Existence 237

3 Sufficient Conditions for Existence 238

4 Efficient Frontier 242

9. Market Demand Functions in the CAPM 245

2 Structure of Market Demand 246

3 Number of CAPM-equilibria 254

10. 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

Main Results 279.

Notes:

Includes bib,iographical references (p. 285-296) and index.

ISBN:

1402073372

OCLC:

51053674