Mathematics of financial obligations:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Mathematical Society
2002
|
| Series: | Translations of mathematical monographs
Vol. 212 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus dem Russ. übers. |
| Physical Description: | IX, 194 S. graph. Darst. |
| ISBN: | 0821829459 |
Staff View
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Record in the Search Index
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| adam_text | TRANSLATIONS OF MATHEMATICAL MONOGRAPHS VOLUME 212 MATHEMATICS OF
FINANCIAL OBLIGATIONS A. V. MEL NIKOV S. N. VOLKOV M. L. NECHAEV |
AMERICAN MATHEMATICAL SOCIETY | PROVIDENCE, RHODE ISLAND CONTENTS
FOREWORD VII MAIN NOTATION IX CHAPTER 1. FINANCIAL SYSTEMS: INNOVATIONS
AND THE RISK CALCULUS 1 §1.1. FINANCIAL SYSTEMS AND THEIR INNOVATION
CHANGES 1 §1.2. GENERAL STATEMENTS IN THE ANALYSIS OF CONTINGENT CLAIMS.
MODELS, METHODS, FACTS 3 § 1.3. DYNAMICS OF FINANCIAL MARKETS: FROM
INCOMPLETE MARKETS TO COM- PLETE MARKETS THROUGH FINANCIAL INNOVATIONS
10 § 1.4. FINANCIAL INNOVATIONS AND INSURANCE RISKS 13 CHAPTER 2. RANDOM
PROCESSES AND THE STOCHASTIC CALCULUS 17 §2.1. RANDOM PROCESSES AND
THEIR DISTRIBUTIONS. THE WIENER PROCESS 17 § 2.2. DIFFUSION PROCESSES.
THE KOLMOGOROV-ITO FORMULA, GIRSANOV S THE- OREM, REPRESENTATIONS OF
MARTINGALES 20 § 2.3. SEMIMARTINGALES AND THE STOCHASTIC CALCULUS 25
CHAPTER 3. HEDGING AND INVESTMENT IN COMPLETE MARKETS 31 §3.1. A
MARTINGALE CHARACTERIZATION OF STRATEGIES AND PERFECT HEDGING 31 § 3.2.
A METHODOLOGY FOR FINDING MARTINGALE MEASURES AND PRICING CON- TINGENT
CLAIMS FOR DIFFERENT MODELS OF A (B, 5)-MARKET 34 § 3.3. A METHODOLOGY
FOR OPTIMAL INVESTMENT AND ITS APPLICATIONS 43 CHAPTER 4. HEDGING AND
INCOMPLETE MARKETS 49 §4.1. A METHODOLOGY FOR SUPERHEDGING 49 §4.2. THE
BLACK-SCHOLES MODEL WITH STOCHASTIC VOLATILITY 52 § 4.3. ESTIMATION OF
VOLATILITY 61 CHAPTER 5. MARKETS WITH STRUCTURAL CONSTRAINTS AND
TRANSACTION COSTS 65 §5.1. CALCULATIONS IN MODELS OF MARKETS WITH
STRUCTURAL CONSTRAINTS: A GENERAL METHODOLOGY AND ITS CONCRETE
REALIZATION 65 §5.2. HEDGING AND INVESTMENT WITH TRANSACTION COSTS 87
§5.3. APPENDIX: EXAMPLES OF THE SIMULATION OF HEDGING STRATEGIES 92
CHAPTER 6. IMPERFECT FORMS OF HEDGING 97 §6.1. MEAN-VARIANCE HEDGING 97
§6.2. QUANTILE HEDGING 104 CHAPTER 7. DYNAMIC CONTINGENT CLAIMS AND
AMERICAN OPTIONS 121 VI CONTENTS § 7.1. PRICING DYNAMIC CONTINGENT
CLAIMS AND THE OPTIMAL STOPPING PROB- LEM 121 § 7.2. CONCRETIZATION OF
OPTION CALCULATIONS AND CLOSED ANALYTIC FORMULAS FOR PRICES AND
STRATEGIES 126 § 7.3. QUANTILE HEDGING OF DYNAMIC CONTINGENT CLAIMS 132
CHAPTER 8. ANALYSIS OF BOND CONTINGENT CLAIMS 139 § 8.1. MODELS OF THE
TERM STRUCTURE OF INTEREST RATES 139 § 8.2. HEDGING ON A BOND MARKET 144
§ 8.3. INVESTING IN A BOND MARKET 153 CHAPTER 9. ECONOMICS OF INSURANCE
AND FINANCE: CONVERGENCE OF QUANTITA- TIVE METHODS OF CALCULATIONS 159
§9.1. NON-LIFE INSURANCE. TRADITIONAL ACTUARIAL PRINCIPLES FOR
CALCULAT- ING PREMIUMS AND THE FINANCIAL NO-ARBITRAGE PRINCIPLE IN A
MODEL OF COLLECTIVE RISK 159 § 9.2. LIFE INSURANCE. MORTALITY TABLES.
CALCULATION OF PREMIUMS AND RESERVES IN TRADITIONAL AND INNOVATION
INSURANCE SCHEMES 167 § 9.3. ESTIMATION OF THE RUIN PROBABILITY 171 §
9.4. CATASTROPHE RISKS AND REINSURANCE OF THEM ON FINANCIAL MARKETS 176
BIBLIOGRAPHICAL NOTES 181 BIBLIOGRAPHY 185 SUBJECT INDEX 191
|
| adam_txt |
TRANSLATIONS OF MATHEMATICAL MONOGRAPHS VOLUME 212 MATHEMATICS OF
FINANCIAL OBLIGATIONS A. V. MEL'NIKOV S. N. VOLKOV M. L. NECHAEV |
AMERICAN MATHEMATICAL SOCIETY | PROVIDENCE, RHODE ISLAND CONTENTS
FOREWORD VII MAIN NOTATION IX CHAPTER 1. FINANCIAL SYSTEMS: INNOVATIONS
AND THE RISK CALCULUS 1 §1.1. FINANCIAL SYSTEMS AND THEIR INNOVATION
CHANGES 1 §1.2. GENERAL STATEMENTS IN THE ANALYSIS OF CONTINGENT CLAIMS.
MODELS, METHODS, FACTS 3 § 1.3. DYNAMICS OF FINANCIAL MARKETS: FROM
INCOMPLETE MARKETS TO COM- PLETE MARKETS THROUGH FINANCIAL INNOVATIONS
10 § 1.4. FINANCIAL INNOVATIONS AND INSURANCE RISKS 13 CHAPTER 2. RANDOM
PROCESSES AND THE STOCHASTIC CALCULUS 17 §2.1. RANDOM PROCESSES AND
THEIR DISTRIBUTIONS. THE WIENER PROCESS 17 § 2.2. DIFFUSION PROCESSES.
THE KOLMOGOROV-ITO FORMULA, GIRSANOV'S THE- OREM, REPRESENTATIONS OF
MARTINGALES 20 § 2.3. SEMIMARTINGALES AND THE STOCHASTIC CALCULUS 25
CHAPTER 3. HEDGING AND INVESTMENT IN COMPLETE MARKETS 31 §3.1. A
MARTINGALE CHARACTERIZATION OF STRATEGIES AND PERFECT HEDGING 31 § 3.2.
A METHODOLOGY FOR FINDING MARTINGALE MEASURES AND PRICING CON- TINGENT
CLAIMS FOR DIFFERENT MODELS OF A (B, 5)-MARKET 34 § 3.3. A METHODOLOGY
FOR OPTIMAL INVESTMENT AND ITS APPLICATIONS 43 CHAPTER 4. HEDGING AND
INCOMPLETE MARKETS 49 §4.1. A METHODOLOGY FOR SUPERHEDGING 49 §4.2. THE
BLACK-SCHOLES MODEL WITH STOCHASTIC VOLATILITY 52 § 4.3. ESTIMATION OF
VOLATILITY 61 CHAPTER 5. MARKETS WITH STRUCTURAL CONSTRAINTS AND
TRANSACTION COSTS 65 §5.1. CALCULATIONS IN MODELS OF MARKETS WITH
STRUCTURAL CONSTRAINTS: A GENERAL METHODOLOGY AND ITS CONCRETE
REALIZATION 65 §5.2. HEDGING AND INVESTMENT WITH TRANSACTION COSTS 87
§5.3. APPENDIX: EXAMPLES OF THE SIMULATION OF HEDGING STRATEGIES 92
CHAPTER 6. IMPERFECT FORMS OF HEDGING 97 §6.1. MEAN-VARIANCE HEDGING 97
§6.2. QUANTILE HEDGING 104 CHAPTER 7. DYNAMIC CONTINGENT CLAIMS AND
AMERICAN OPTIONS 121 VI CONTENTS § 7.1. PRICING DYNAMIC CONTINGENT
CLAIMS AND THE OPTIMAL STOPPING PROB- LEM 121 § 7.2. CONCRETIZATION OF
OPTION CALCULATIONS AND CLOSED ANALYTIC FORMULAS FOR PRICES AND
STRATEGIES 126 § 7.3. QUANTILE HEDGING OF DYNAMIC CONTINGENT CLAIMS 132
CHAPTER 8. ANALYSIS OF "BOND" CONTINGENT CLAIMS 139 § 8.1. MODELS OF THE
TERM STRUCTURE OF INTEREST RATES 139 § 8.2. HEDGING ON A BOND MARKET 144
§ 8.3. INVESTING IN A BOND MARKET 153 CHAPTER 9. ECONOMICS OF INSURANCE
AND FINANCE: CONVERGENCE OF QUANTITA- TIVE METHODS OF CALCULATIONS 159
§9.1. "NON-LIFE" INSURANCE. TRADITIONAL ACTUARIAL PRINCIPLES FOR
CALCULAT- ING PREMIUMS AND THE FINANCIAL NO-ARBITRAGE PRINCIPLE IN A
MODEL OF COLLECTIVE RISK 159 § 9.2. LIFE INSURANCE. MORTALITY TABLES.
CALCULATION OF PREMIUMS AND RESERVES IN TRADITIONAL AND INNOVATION
INSURANCE SCHEMES 167 § 9.3. ESTIMATION OF THE RUIN PROBABILITY 171 §
9.4. CATASTROPHE RISKS AND REINSURANCE OF THEM ON FINANCIAL MARKETS 176
BIBLIOGRAPHICAL NOTES 181 BIBLIOGRAPHY 185 SUBJECT INDEX 191 |
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| author | Melʹnikov, Aleksandr V. 1953- Volkov, Sergej N. 1972- Nečaev, Michail L. 1972- |
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| author_role | aut aut aut |
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| dewey-ones | 332 - Financial economics |
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| dewey-search | 332.6/01/51 21 |
| dewey-sort | 3332.6 11 251 221 |
| dewey-tens | 330 - Economics |
| discipline | Mathematik Wirtschaftswissenschaften |
| discipline_str_mv | Mathematik Wirtschaftswissenschaften |
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| illustrated | Illustrated |
| index_date | 2024-07-02T22:38:11Z |
| indexdate | 2024-07-09T21:24:35Z |
| institution | BVB |
| isbn | 0821829459 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016879308 |
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| physical | IX, 194 S. graph. Darst. |
| publishDate | 2002 |
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| publisher | American Mathematical Society |
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| series | Translations of mathematical monographs |
| series2 | Translations of mathematical monographs |
| spelling | Melʹnikov, Aleksandr V. 1953- Verfasser (DE-588)128679778 aut Matematika finansovych objazatel'stv Mathematics of financial obligations A. V. Mel'nikov ; S. N. Volkov ; M. L. Nechaev Providence, RI American Mathematical Society 2002 IX, 194 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Translations of mathematical monographs Vol. 212 Aus dem Russ. übers. Mathematik Mathematisches Modell Investments -- Mathematics Stochastic analysis Hedging (Finance) -- Mathematical models Insurance -- Mathematics Versicherungsmathematik (DE-588)4063194-1 gnd rswk-swf Finanzmathematik (DE-588)4017195-4 gnd rswk-swf Finanzmathematik (DE-588)4017195-4 s DE-604 Versicherungsmathematik (DE-588)4063194-1 s Volkov, Sergej N. 1972- Verfasser (DE-588)128679824 aut Nečaev, Michail L. 1972- Verfasser (DE-588)128679840 aut Translations of mathematical monographs Vol. 212 (DE-604)BV000002394 212 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016879308&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Melʹnikov, Aleksandr V. 1953- Volkov, Sergej N. 1972- Nečaev, Michail L. 1972- Mathematics of financial obligations Translations of mathematical monographs Mathematik Mathematisches Modell Investments -- Mathematics Stochastic analysis Hedging (Finance) -- Mathematical models Insurance -- Mathematics Versicherungsmathematik (DE-588)4063194-1 gnd Finanzmathematik (DE-588)4017195-4 gnd |
| subject_GND | (DE-588)4063194-1 (DE-588)4017195-4 |
| title | Mathematics of financial obligations |
| title_alt | Matematika finansovych objazatel'stv |
| title_auth | Mathematics of financial obligations |
| title_exact_search | Mathematics of financial obligations |
| title_exact_search_txtP | Mathematics of financial obligations |
| title_full | Mathematics of financial obligations A. V. Mel'nikov ; S. N. Volkov ; M. L. Nechaev |
| title_fullStr | Mathematics of financial obligations A. V. Mel'nikov ; S. N. Volkov ; M. L. Nechaev |
| title_full_unstemmed | Mathematics of financial obligations A. V. Mel'nikov ; S. N. Volkov ; M. L. Nechaev |
| title_short | Mathematics of financial obligations |
| title_sort | mathematics of financial obligations |
| topic | Mathematik Mathematisches Modell Investments -- Mathematics Stochastic analysis Hedging (Finance) -- Mathematical models Insurance -- Mathematics Versicherungsmathematik (DE-588)4063194-1 gnd Finanzmathematik (DE-588)4017195-4 gnd |
| topic_facet | Mathematik Mathematisches Modell Investments -- Mathematics Stochastic analysis Hedging (Finance) -- Mathematical models Insurance -- Mathematics Versicherungsmathematik Finanzmathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016879308&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000002394 |
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