General Equilibrium Foundations of Finance: Structure of Incomplete Markets ModelsSpringer Science & Business Media, 2002 - 299 sidor 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. |
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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General Equilibrium Foundations of Finance: Structure of Incomplete Markets ... Thorsten Hens,Beate Pilgrim Begränsad förhandsgranskning - 2013 |
General Equilibrium Foundations of Finance: Structure of Incomplete Markets ... Thorsten Hens,Beate Pilgrim Ingen förhandsgranskning - 2010 |
General Equilibrium Foundations of Finance Thorsten Hens,Beate Pilgrim Ingen förhandsgranskning - 2014 |
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absolute risk aversion agent allocation arbitrage arg max Arrow-Debreu model asset matrix asset prices asset structure Assumption 1.5 boundary behavior budget set CAPM Chapter cheaper point assumption collinear competitive equilibria constraint consumers consumption consumption set continuously differentiable Corollary decision problem defined DEFINITION equilibrium model equilibrium price equivalent example excess demand functions exists expected utility hypothesis financial markets FM equilibrium GEI-economy GEI-model given Hence implicit function theorem implies incomplete markets indifference curves initial endowments investors Lemma linear Magill and Quinzii market demand market excess demand market portfolio Mas-Colell maximization problem mean-variance Mitjushin-Polterovich no-arbitrage non-negative number of equilibria Pareto-efficient payoff price vector proof Proposition Qnorm rank restricted riskless asset satisfies Assumption strict gross substitution strictly monotone strictly positive strictly quasi-concave Theorem Ui wi unique equilibrium utility function Ui
Populära avsnitt
Sida 287 - Thomas E. Copeland and J. Fred Weston, Financial Theory and Corporate Policy 198-199 (3d ed.
Sida 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.