Mathematical finance and probability: a discrete introduction
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Basel [u.a.]
Birkhäuser
2003
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 328 S. Ill. |
| ISBN: | 3764369213 0817669213 |
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Record in the Search Index
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| adam_text | PABLO KOCH MEDINA SANDRO MERINO MATHEMATICAL FINANCE AND PROBABILITY A
DISCRETE INTRODUCTION BIRKHAUSER VERLAG BASEL * BOSTON * BERLIN CONTENTS
1 INTRODUCTION 1 2 A SHORT PRIMER ON FINANCE 7 2.1 A ONE-PERIOD MODEL
WITH TWO STATES AND TWO SECURITIES 7 2.2 LAW OF ONE PRICE, COMPLETENESS
AND FAIR VALUE 21 2.3 ARBITRAGE AND POSITIVITY OF THE PRICING FUNCTIONAL
25 2.4 RISK-ADJUSTED PROBABILITY MEASURES 28 2.5 EQUIVALENT MARTINGALE
MEASURES 33 2.6 OPTIONS AND FORWARDS 36 3 POSITIVE LINEAR FUNCTIONALS 41
3.1 LINEAR FUNCTIONALS 41 3.2 POSITIVE LINEAR FUNCTIONALS INTRODUCED 43
3.3 SEPARATION THEOREMS 48 3.4 EXTENSION OF POSITIVE LINEAR FUNCTIONALS
57 3.5 OPTIMAL POSITIVE EXTENSIONS* 59 4 FINITE PROBABILITY SPACES 73
4.1 FINITE PROBABILITY SPACES 73 4.2 LAPLACE EXPERIMENTS 76 4.3
ELEMENTARY COMBINATORIAL PROBLEMS 77 4.4 CONDITIONING 82 4.5 MORE ON URN
MODELS 83 5 RANDOM VARIABLES 89 5.1 RANDOM VARIABLES AND THEIR
DISTRIBUTIONS 89 5.2 THE VECTOR SPACE OF RANDOM VARIABLES 93 5.3
POSITIVITY ON L(IL) 95 5.4 EXPECTED VALUE AND VARIANCE 97 5.5 TWO
EXAMPLES 103 5.6 THE L 2 -STRUCTURE ON I(FI) 105 VI CONTENTS 6 GENERAL
ONE-PERIOD MODELS 111 6.1 THE ELEMENTS OF THE MODEL ILL 6.2
ATTAINABILITY AND REPLICATION 115 6.3 THE LAW OF ONE PRICE AND LINEAR
PRICING FUNCTIONALS 116 6.4 ARBITRAGE AND STRONGLY POSITIVE PRICING
FUNCTIONALS 118 6.5 COMPLETENESS 120 6.6 THE FUNDAMENTAL THEOREMS OF
ASSET PRICING 121 6.7 FAIR VALUE IN INCOMPLETE MARKETS* 127 7
INFORMATION AND RANDOMNESS 129 7.1 INFORMATION, PARTITIONS AND ALGEBRAS
129 7.2 RANDOM VARIABLES AND MEASURABILITY 135 7.3 LINEAR SUBSPACES OF
L(Q) AND MEASURABILITY 136 7.4 RANDOM VARIABLES AND INFORMATION 139 7.5
INFORMATION STRUCTURES AND FLOW OF INFORMATION 142 7.6 STOCHASTIC
PROCESSES AND INFORMATION STRUCTURES 144 8 INDEPENDENCE 147 8.1
INDEPENDENCE OF EVENTS 147 8.2 INDEPENDENCE OF RANDOM VARIABLES 153 8.3
EXPECTATIONS, VARIANCE AND INDEPENDENCE 155 8.4 SEQUENCES OF INDEPENDENT
EXPERIMENTS 156 9 MULTI-PERIOD MODELS: THE MAIN ISSUES 161 9.1 THE
ELEMENTS OF THE MODEL 161 9.2 PORTFOLIOS AND TRADING STRATEGIES 165 9.3
ATTAINABILITY AND REPLICATION 168 9.4 THE LAW OF ONE PRICE AND LINEAR
PRICING FUNCTIONALS 168 9.5 NO-ARBITRAGE AND STRONGLY POSITIVE PRICING
FUNCTIONALS 170 9.6 COMPLETENESS 174 9.7 STRONGLY POSITIVE EXTENSIONS OF
THE PRICING FUNCTIONAL 175 9.8 FAIR VALUE IN INCOMPLETE MARKETS* 176 10
CONDITIONING AND MARTINGALES 179 10.1 CONDITIONAL EXPECTATION 179 10.2
CONDITIONAL EXPECTATIONS AND Z/2-ORTHOGONALITY 186 10.3 MARTINGALES 187
11 THE FUNDAMENTAL THEOREMS OF ASSET PRICING 191 11.1 CHANGE OF
NUMERAIRE AND DISCOUNTING 192 11.2 MARTINGALES AND ASSET PRICES 193 11.3
THE FUNDAMENTAL THEOREMS OF ASSET PRICING 198 11.4 RISK-ADJUSTED AND
FORWARD-NEUTRAL MEASURES 198 CONTENTS VII 12 THE COX-ROSS-RUBINSTEIN
MODEL 201 12.1 THE COX-ROSS-RUBINSTEIN ECONOMY 201 12.2 PARAMETRIZING
THE MODEL 205 12.3 EQUIVALENT MARTINGALE MEASURES: UNIQUENESS 208 12.4
EQUIVALENT MARTINGALE MEASURES: EXISTENCE 210 12.5 PRICING IN THE
COX-ROSS-RUBINSTEIN ECONOMY 212 12.6 HEDGING IN THE COX-ROSS-RUBINSTEIN
ECONOMY 215 12.7 EUROPEAN CALL AND PUT OPTIONS 216 13 THE CENTRAL LIMIT
THEOREM 221 13.1 MOTIVATING EXAMPLE 221 13.2 GENERAL PROBABILITY SPACES
224 13.3 RANDOM VARIABLES 230 13.4 WEAK CONVERGENCE OF A SEQUENCE OF
RANDOM VARIABLES 238 13.5 THE THEOREM OF DE MOIVRE-LAPLACE 240 14 THE
BLACK-SCHOLES FORMULA 247 14.1 LIMITING BEHAVIOR OF A
COX-ROSS-RUBINSTEIN ECONOMY 247 14.2 THE BLACK-SCHOLES FORMULA 252 15
OPTIMAL STOPPING 257 15.1 STOPPING TIMES INTRODUCED 257 15.2 SAMPLING A
PROCESS BY A STOPPING TIME 260 15.3 OPTIMAL STOPPING 262 15.4 MARKOV
CHAINS AND THE SNELL ENVELOPE 271 16 AMERICAN CLAIMS 277 16.1 THE
UNDERLYING ECONOMY 277 16.2 AMERICAN CLAIMS INTRODUCED 278 16.3 THE
BUYER S PERSPECTIVE: OPTIMAL EXERCISE 280 16.4 THE SELLER S PERSPECTIVE:
HEDGING 281 16.5 THE FAIR VALUE OF AN AMERICAN CLAIM 284 16.6 COMPARING
AMERICAN TO EUROPEAN OPTIONS 285 16.7 HOMOGENEOUS MARKOV PROCESSES 286 A
EUCLIDEAN SPACE AND LINEAR ALGEBRA 297 A.I VECTOR SPACES 297 A.2 INNER
PRODUCT AND EUCLIDEAN SPACES 301 A.3 TOPOLOGY IN EUCLIDEAN SPACE 302 A.4
LINEAR OPERATORS 304 A.5 LINEAR EQUATIONS 306 B PROOF OF THE THEOREM OF
DE MOIVRE*LAPLACE 309 B.I PRELIMINARY RESULTS 310 B.2 PROOF OF THE
THEOREM OF DE MOIVRE-LAPLACE 318
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| dewey-tens | 330 - Economics |
| discipline | Mathematik Wirtschaftswissenschaften |
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| language | English |
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| spelling | Koch Medina, Pablo Verfasser aut Mathematical finance and probability a discrete introduction Pablo Koch Medina ; Sandro Merino Basel [u.a.] Birkhäuser 2003 VIII, 328 S. Ill. txt rdacontent n rdamedia nc rdacarrier Effecten gtt Financieel management gtt Investissements - Mathématiques Investissements - Modèles mathématiques Martingalen gtt Probabilités Valeurs mobilières - Modèles mathématiques Waarschijnlijkheid (statistiek) gtt Wiskundige modellen gtt Mathematik Mathematisches Modell Investments -- Mathematics Investments -- Mathematical models Probabilities Securities -- Mathematical models Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Finanzmathematik (DE-588)4017195-4 gnd rswk-swf Finanzmathematik (DE-588)4017195-4 s Wahrscheinlichkeitstheorie (DE-588)4079013-7 s DE-604 Merino, Sandro Verfasser aut HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010062033&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Koch Medina, Pablo Merino, Sandro Mathematical finance and probability a discrete introduction Effecten gtt Financieel management gtt Investissements - Mathématiques Investissements - Modèles mathématiques Martingalen gtt Probabilités Valeurs mobilières - Modèles mathématiques Waarschijnlijkheid (statistiek) gtt Wiskundige modellen gtt Mathematik Mathematisches Modell Investments -- Mathematics Investments -- Mathematical models Probabilities Securities -- Mathematical models Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Finanzmathematik (DE-588)4017195-4 gnd |
| subject_GND | (DE-588)4079013-7 (DE-588)4017195-4 |
| title | Mathematical finance and probability a discrete introduction |
| title_auth | Mathematical finance and probability a discrete introduction |
| title_exact_search | Mathematical finance and probability a discrete introduction |
| title_full | Mathematical finance and probability a discrete introduction Pablo Koch Medina ; Sandro Merino |
| title_fullStr | Mathematical finance and probability a discrete introduction Pablo Koch Medina ; Sandro Merino |
| title_full_unstemmed | Mathematical finance and probability a discrete introduction Pablo Koch Medina ; Sandro Merino |
| title_short | Mathematical finance and probability |
| title_sort | mathematical finance and probability a discrete introduction |
| title_sub | a discrete introduction |
| topic | Effecten gtt Financieel management gtt Investissements - Mathématiques Investissements - Modèles mathématiques Martingalen gtt Probabilités Valeurs mobilières - Modèles mathématiques Waarschijnlijkheid (statistiek) gtt Wiskundige modellen gtt Mathematik Mathematisches Modell Investments -- Mathematics Investments -- Mathematical models Probabilities Securities -- Mathematical models Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Finanzmathematik (DE-588)4017195-4 gnd |
| topic_facet | Effecten Financieel management Investissements - Mathématiques Investissements - Modèles mathématiques Martingalen Probabilités Valeurs mobilières - Modèles mathématiques Waarschijnlijkheid (statistiek) Wiskundige modellen Mathematik Mathematisches Modell Investments -- Mathematics Investments -- Mathematical models Probabilities Securities -- Mathematical models Wahrscheinlichkeitstheorie Finanzmathematik |
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