Hypermodels in mathematical finance :: modelling via infinitesimal analysis /
At the beginning of the new millennium, two unstoppable processes aretaking place in the world: (1) globalization of the economy; (2)information revolution. As a consequence, there is greaterparticipation of the world population in capital market investment, such as bonds and stocks and their deriva...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
River Edge, N.J. :
World Scientific,
©2003.
|
| Schlagworte: | |
| Online-Zugang: | DE-862 DE-863 |
| Zusammenfassung: | At the beginning of the new millennium, two unstoppable processes aretaking place in the world: (1) globalization of the economy; (2)information revolution. As a consequence, there is greaterparticipation of the world population in capital market investment, such as bonds and stocks and their derivatives. |
| Beschreibung: | 1 online resource (xiii, 298 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (pages 289-294) and index. |
| ISBN: | 9812564527 9789812564528 9789810244286 9810244282 1281876909 9781281876904 9786611876906 6611876901 |
Internformat
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| 245 | 1 | 0 | |a Hypermodels in mathematical finance : |b modelling via infinitesimal analysis / |c Siu-Ah Ng. |
| 260 | |a River Edge, N.J. : |b World Scientific, |c ©2003. | ||
| 300 | |a 1 online resource (xiii, 298 pages) : |b illustrations | ||
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| 504 | |a Includes bibliographical references (pages 289-294) and index. | ||
| 505 | 0 | |a Cover -- Preface -- Contents -- Notation and Convention -- Chapter 1 Basic Concepts and Practice in Finance -- 1.1 Introducing mathematical finance -- 1.2 Basic securities -- 1.2.1 Stocks -- 1.2.2 Bonds -- 1.2.3 Others: bank accounts, currencies and commodities -- 1.3 Derivative securities -- 1.3.1 Options -- 1.3.2 Other derivative securities -- 1.4 Theory and practice -- Chapter 2 Infinitesimal Analysis and Hypermodels -- 2.1 Motivations -- 2.2 Hypermodels and analysis -- Chapter 3 Absence of Arbitrage -- 3.1 Introduction -- 3.2 Absence of arbitrage and the binary tree hypermodel -- 3.2.1 A mini-model -- 3.2.2 Binary tree model -- 3.2.3 Binary tree hypermodel -- 3.2.4 Finiteness of stock prices -- 3.2.5 Risk-neutral measure for binary tree hypermodel -- 3.3 Black-Scholes type PDE from virtually arbitrage-free -- 3.3.1 Virtually arbitrage free -- Chapter 4 Explicit Option Pricing -- 4.1 From hypermodel to PDE -- 4.1.1 Barrier conditions for derivative claims -- 4.1.2 Tangible price processes -- 4.1.3 Differential equations in a hypermodel -- 4.1.4 Black-Scholes type PDE -- 4.2 Pricing options explicitly -- 4.2.1 The classical Black-Scholes formula -- 4.3 The barrier option -- 4.4 The American option -- Chapter 5 Pricing with Binary Tree Hypermodels -- 5.1 Hypermodels for the Cox-Ross-Rubinstein approach -- 5.2 The CRR matrix and Examples -- Chapter 6 Further Applications -- 6.1 Sensitivity analysis -- 6.1.1 The Greeks -- 6.1.2 Computing the Greeks from translating -- 6.2 Implied volatility -- 6.3 Term structure of interest rates -- Chapter 7 The Mathematics of Hypermodels -- 7.1 Mathematical logic and Classical Hyperanalysis -- 7.1.1 Logic and hypermodels *R -- 7.1.2 Construction of *R using the compactness theorem -- 7.1.3 Construction of *R using ultrapowers -- 7.1.4 Some basic properties of hypermodel *R -- 7.1.5 Hypermodels of R in richer languages -- 7.1.6 Some examples -- 7.1.7 References -- 7.2 The hyperuniverse -- 7.2.1 Doing mathematics in the language of set theory -- 7.2.2 Hyperuniverse and the hyperextension -- 7.2.3 The existence of the hyperextension -- 7.2.4 Applications and examples -- 7.2.5 References -- 7.3 Hyperanalysis of probability -- 7.3.1 The Loeb measure construction -- 7.3.2 Loeb integration theory -- 7.3.3 Some examples -- 7.4 Hypermodels of Brownian Motion -- 7.4.1 Anderson's discrete hypermodel of Brownian motion -- 7.4.2 Some * continuous hypermodels of Brownian motion -- 7.4.3 Some examples -- 7.5 Itô Integral and Stochastic Differential Equations -- 7.5.1 Some general remarks -- 7.5.2 Wiener integral and Itô integral -- 7.5.3 Itô's lemma and the Stratonovitch integral -- 7.6 Solving Stochastic differential equations -- 7.7 Malliavin calculus -- 7.8 White noise analysis -- 7.9 Universality and homogeneity properties of hyperfinite models -- Appendix. | |
| 588 | 0 | |a Print version record. | |
| 520 | |a At the beginning of the new millennium, two unstoppable processes aretaking place in the world: (1) globalization of the economy; (2)information revolution. As a consequence, there is greaterparticipation of the world population in capital market investment, such as bonds and stocks and their derivatives. | ||
| 546 | |a English. | ||
| 650 | 0 | |a Investments |x Mathematical models. |0 http://id.loc.gov/authorities/subjects/sh85067718 | |
| 650 | 0 | |a Securities |x Mathematical models. | |
| 650 | 0 | |a Risk management |x Mathematical models. | |
| 650 | 6 | |a Investissements |x Modèles mathématiques. | |
| 650 | 6 | |a Gestion du risque |x Modèles mathématiques. | |
| 650 | 7 | |a BUSINESS & ECONOMICS |x Investments & Securities |x General. |2 bisacsh | |
| 650 | 7 | |a Investments |x Mathematical models |2 fast | |
| 650 | 7 | |a Risk management |x Mathematical models |2 fast | |
| 650 | 7 | |a Securities |x Mathematical models |2 fast | |
| 758 | |i has work: |a Hypermodels in mathematical finance (Text) |1 https://id.oclc.org/worldcat/entity/E39PCGCJGC4gCxvH6k333jh7f3 |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Ng, Siu-Ah. |t Hypermodels in mathematical finance. |d River Edge, N.J. : World Scientific, ©2003 |w (DLC) 52066471 |
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Datensatz im Suchindex
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| author | Ng, Siu-Ah |
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| author_facet | Ng, Siu-Ah |
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| contents | Cover -- Preface -- Contents -- Notation and Convention -- Chapter 1 Basic Concepts and Practice in Finance -- 1.1 Introducing mathematical finance -- 1.2 Basic securities -- 1.2.1 Stocks -- 1.2.2 Bonds -- 1.2.3 Others: bank accounts, currencies and commodities -- 1.3 Derivative securities -- 1.3.1 Options -- 1.3.2 Other derivative securities -- 1.4 Theory and practice -- Chapter 2 Infinitesimal Analysis and Hypermodels -- 2.1 Motivations -- 2.2 Hypermodels and analysis -- Chapter 3 Absence of Arbitrage -- 3.1 Introduction -- 3.2 Absence of arbitrage and the binary tree hypermodel -- 3.2.1 A mini-model -- 3.2.2 Binary tree model -- 3.2.3 Binary tree hypermodel -- 3.2.4 Finiteness of stock prices -- 3.2.5 Risk-neutral measure for binary tree hypermodel -- 3.3 Black-Scholes type PDE from virtually arbitrage-free -- 3.3.1 Virtually arbitrage free -- Chapter 4 Explicit Option Pricing -- 4.1 From hypermodel to PDE -- 4.1.1 Barrier conditions for derivative claims -- 4.1.2 Tangible price processes -- 4.1.3 Differential equations in a hypermodel -- 4.1.4 Black-Scholes type PDE -- 4.2 Pricing options explicitly -- 4.2.1 The classical Black-Scholes formula -- 4.3 The barrier option -- 4.4 The American option -- Chapter 5 Pricing with Binary Tree Hypermodels -- 5.1 Hypermodels for the Cox-Ross-Rubinstein approach -- 5.2 The CRR matrix and Examples -- Chapter 6 Further Applications -- 6.1 Sensitivity analysis -- 6.1.1 The Greeks -- 6.1.2 Computing the Greeks from translating -- 6.2 Implied volatility -- 6.3 Term structure of interest rates -- Chapter 7 The Mathematics of Hypermodels -- 7.1 Mathematical logic and Classical Hyperanalysis -- 7.1.1 Logic and hypermodels *R -- 7.1.2 Construction of *R using the compactness theorem -- 7.1.3 Construction of *R using ultrapowers -- 7.1.4 Some basic properties of hypermodel *R -- 7.1.5 Hypermodels of R in richer languages -- 7.1.6 Some examples -- 7.1.7 References -- 7.2 The hyperuniverse -- 7.2.1 Doing mathematics in the language of set theory -- 7.2.2 Hyperuniverse and the hyperextension -- 7.2.3 The existence of the hyperextension -- 7.2.4 Applications and examples -- 7.2.5 References -- 7.3 Hyperanalysis of probability -- 7.3.1 The Loeb measure construction -- 7.3.2 Loeb integration theory -- 7.3.3 Some examples -- 7.4 Hypermodels of Brownian Motion -- 7.4.1 Anderson's discrete hypermodel of Brownian motion -- 7.4.2 Some * continuous hypermodels of Brownian motion -- 7.4.3 Some examples -- 7.5 Itô Integral and Stochastic Differential Equations -- 7.5.1 Some general remarks -- 7.5.2 Wiener integral and Itô integral -- 7.5.3 Itô's lemma and the Stratonovitch integral -- 7.6 Solving Stochastic differential equations -- 7.7 Malliavin calculus -- 7.8 White noise analysis -- 7.9 Universality and homogeneity properties of hyperfinite models -- Appendix. |
| ctrlnum | (OCoLC)228115550 |
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| dewey-ones | 332 - Financial economics |
| dewey-raw | 332.6 |
| dewey-search | 332.6 |
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| discipline | Wirtschaftswissenschaften |
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analysis -- Chapter 3 Absence of Arbitrage -- 3.1 Introduction -- 3.2 Absence of arbitrage and the binary tree hypermodel -- 3.2.1 A mini-model -- 3.2.2 Binary tree model -- 3.2.3 Binary tree hypermodel -- 3.2.4 Finiteness of stock prices -- 3.2.5 Risk-neutral measure for binary tree hypermodel -- 3.3 Black-Scholes type PDE from virtually arbitrage-free -- 3.3.1 Virtually arbitrage free -- Chapter 4 Explicit Option Pricing -- 4.1 From hypermodel to PDE -- 4.1.1 Barrier conditions for derivative claims -- 4.1.2 Tangible price processes -- 4.1.3 Differential equations in a hypermodel -- 4.1.4 Black-Scholes type PDE -- 4.2 Pricing options explicitly -- 4.2.1 The classical Black-Scholes formula -- 4.3 The barrier option -- 4.4 The American option -- Chapter 5 Pricing with Binary Tree Hypermodels -- 5.1 Hypermodels for the Cox-Ross-Rubinstein approach -- 5.2 The CRR matrix and Examples -- Chapter 6 Further Applications -- 6.1 Sensitivity analysis -- 6.1.1 The Greeks -- 6.1.2 Computing the Greeks from translating -- 6.2 Implied volatility -- 6.3 Term structure of interest rates -- Chapter 7 The Mathematics of Hypermodels -- 7.1 Mathematical logic and Classical Hyperanalysis -- 7.1.1 Logic and hypermodels *R -- 7.1.2 Construction of *R using the compactness theorem -- 7.1.3 Construction of *R using ultrapowers -- 7.1.4 Some basic properties of hypermodel *R -- 7.1.5 Hypermodels of R in richer languages -- 7.1.6 Some examples -- 7.1.7 References -- 7.2 The hyperuniverse -- 7.2.1 Doing mathematics in the language of set theory -- 7.2.2 Hyperuniverse and the hyperextension -- 7.2.3 The existence of the hyperextension -- 7.2.4 Applications and examples -- 7.2.5 References -- 7.3 Hyperanalysis of probability -- 7.3.1 The Loeb measure construction -- 7.3.2 Loeb integration theory -- 7.3.3 Some examples -- 7.4 Hypermodels of Brownian Motion -- 7.4.1 Anderson's discrete hypermodel of Brownian motion -- 7.4.2 Some * continuous hypermodels of Brownian motion -- 7.4.3 Some examples 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| id | ZDB-4-EBA-ocn228115550 |
| illustrated | Illustrated |
| indexdate | 2025-04-11T08:36:03Z |
| institution | BVB |
| isbn | 9812564527 9789812564528 9789810244286 9810244282 1281876909 9781281876904 9786611876906 6611876901 |
| language | English |
| oclc_num | 228115550 |
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| spelling | Ng, Siu-Ah. https://id.oclc.org/worldcat/entity/E39PCjB43KhJxBPTrKJgCq4xrC http://id.loc.gov/authorities/names/no2003055658 Hypermodels in mathematical finance : modelling via infinitesimal analysis / Siu-Ah Ng. River Edge, N.J. : World Scientific, ©2003. 1 online resource (xiii, 298 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier data file Includes bibliographical references (pages 289-294) and index. Cover -- Preface -- Contents -- Notation and Convention -- Chapter 1 Basic Concepts and Practice in Finance -- 1.1 Introducing mathematical finance -- 1.2 Basic securities -- 1.2.1 Stocks -- 1.2.2 Bonds -- 1.2.3 Others: bank accounts, currencies and commodities -- 1.3 Derivative securities -- 1.3.1 Options -- 1.3.2 Other derivative securities -- 1.4 Theory and practice -- Chapter 2 Infinitesimal Analysis and Hypermodels -- 2.1 Motivations -- 2.2 Hypermodels and analysis -- Chapter 3 Absence of Arbitrage -- 3.1 Introduction -- 3.2 Absence of arbitrage and the binary tree hypermodel -- 3.2.1 A mini-model -- 3.2.2 Binary tree model -- 3.2.3 Binary tree hypermodel -- 3.2.4 Finiteness of stock prices -- 3.2.5 Risk-neutral measure for binary tree hypermodel -- 3.3 Black-Scholes type PDE from virtually arbitrage-free -- 3.3.1 Virtually arbitrage free -- Chapter 4 Explicit Option Pricing -- 4.1 From hypermodel to PDE -- 4.1.1 Barrier conditions for derivative claims -- 4.1.2 Tangible price processes -- 4.1.3 Differential equations in a hypermodel -- 4.1.4 Black-Scholes type PDE -- 4.2 Pricing options explicitly -- 4.2.1 The classical Black-Scholes formula -- 4.3 The barrier option -- 4.4 The American option -- Chapter 5 Pricing with Binary Tree Hypermodels -- 5.1 Hypermodels for the Cox-Ross-Rubinstein approach -- 5.2 The CRR matrix and Examples -- Chapter 6 Further Applications -- 6.1 Sensitivity analysis -- 6.1.1 The Greeks -- 6.1.2 Computing the Greeks from translating -- 6.2 Implied volatility -- 6.3 Term structure of interest rates -- Chapter 7 The Mathematics of Hypermodels -- 7.1 Mathematical logic and Classical Hyperanalysis -- 7.1.1 Logic and hypermodels *R -- 7.1.2 Construction of *R using the compactness theorem -- 7.1.3 Construction of *R using ultrapowers -- 7.1.4 Some basic properties of hypermodel *R -- 7.1.5 Hypermodels of R in richer languages -- 7.1.6 Some examples -- 7.1.7 References -- 7.2 The hyperuniverse -- 7.2.1 Doing mathematics in the language of set theory -- 7.2.2 Hyperuniverse and the hyperextension -- 7.2.3 The existence of the hyperextension -- 7.2.4 Applications and examples -- 7.2.5 References -- 7.3 Hyperanalysis of probability -- 7.3.1 The Loeb measure construction -- 7.3.2 Loeb integration theory -- 7.3.3 Some examples -- 7.4 Hypermodels of Brownian Motion -- 7.4.1 Anderson's discrete hypermodel of Brownian motion -- 7.4.2 Some * continuous hypermodels of Brownian motion -- 7.4.3 Some examples -- 7.5 Itô Integral and Stochastic Differential Equations -- 7.5.1 Some general remarks -- 7.5.2 Wiener integral and Itô integral -- 7.5.3 Itô's lemma and the Stratonovitch integral -- 7.6 Solving Stochastic differential equations -- 7.7 Malliavin calculus -- 7.8 White noise analysis -- 7.9 Universality and homogeneity properties of hyperfinite models -- Appendix. Print version record. At the beginning of the new millennium, two unstoppable processes aretaking place in the world: (1) globalization of the economy; (2)information revolution. As a consequence, there is greaterparticipation of the world population in capital market investment, such as bonds and stocks and their derivatives. English. Investments Mathematical models. http://id.loc.gov/authorities/subjects/sh85067718 Securities Mathematical models. Risk management Mathematical models. Investissements Modèles mathématiques. Gestion du risque Modèles mathématiques. BUSINESS & ECONOMICS Investments & Securities General. bisacsh Investments Mathematical models fast Risk management Mathematical models fast Securities Mathematical models fast has work: Hypermodels in mathematical finance (Text) https://id.oclc.org/worldcat/entity/E39PCGCJGC4gCxvH6k333jh7f3 https://id.oclc.org/worldcat/ontology/hasWork Print version: Ng, Siu-Ah. Hypermodels in mathematical finance. River Edge, N.J. : World Scientific, ©2003 (DLC) 52066471 |
| spellingShingle | Ng, Siu-Ah Hypermodels in mathematical finance : modelling via infinitesimal analysis / Cover -- Preface -- Contents -- Notation and Convention -- Chapter 1 Basic Concepts and Practice in Finance -- 1.1 Introducing mathematical finance -- 1.2 Basic securities -- 1.2.1 Stocks -- 1.2.2 Bonds -- 1.2.3 Others: bank accounts, currencies and commodities -- 1.3 Derivative securities -- 1.3.1 Options -- 1.3.2 Other derivative securities -- 1.4 Theory and practice -- Chapter 2 Infinitesimal Analysis and Hypermodels -- 2.1 Motivations -- 2.2 Hypermodels and analysis -- Chapter 3 Absence of Arbitrage -- 3.1 Introduction -- 3.2 Absence of arbitrage and the binary tree hypermodel -- 3.2.1 A mini-model -- 3.2.2 Binary tree model -- 3.2.3 Binary tree hypermodel -- 3.2.4 Finiteness of stock prices -- 3.2.5 Risk-neutral measure for binary tree hypermodel -- 3.3 Black-Scholes type PDE from virtually arbitrage-free -- 3.3.1 Virtually arbitrage free -- Chapter 4 Explicit Option Pricing -- 4.1 From hypermodel to PDE -- 4.1.1 Barrier conditions for derivative claims -- 4.1.2 Tangible price processes -- 4.1.3 Differential equations in a hypermodel -- 4.1.4 Black-Scholes type PDE -- 4.2 Pricing options explicitly -- 4.2.1 The classical Black-Scholes formula -- 4.3 The barrier option -- 4.4 The American option -- Chapter 5 Pricing with Binary Tree Hypermodels -- 5.1 Hypermodels for the Cox-Ross-Rubinstein approach -- 5.2 The CRR matrix and Examples -- Chapter 6 Further Applications -- 6.1 Sensitivity analysis -- 6.1.1 The Greeks -- 6.1.2 Computing the Greeks from translating -- 6.2 Implied volatility -- 6.3 Term structure of interest rates -- Chapter 7 The Mathematics of Hypermodels -- 7.1 Mathematical logic and Classical Hyperanalysis -- 7.1.1 Logic and hypermodels *R -- 7.1.2 Construction of *R using the compactness theorem -- 7.1.3 Construction of *R using ultrapowers -- 7.1.4 Some basic properties of hypermodel *R -- 7.1.5 Hypermodels of R in richer languages -- 7.1.6 Some examples -- 7.1.7 References -- 7.2 The hyperuniverse -- 7.2.1 Doing mathematics in the language of set theory -- 7.2.2 Hyperuniverse and the hyperextension -- 7.2.3 The existence of the hyperextension -- 7.2.4 Applications and examples -- 7.2.5 References -- 7.3 Hyperanalysis of probability -- 7.3.1 The Loeb measure construction -- 7.3.2 Loeb integration theory -- 7.3.3 Some examples -- 7.4 Hypermodels of Brownian Motion -- 7.4.1 Anderson's discrete hypermodel of Brownian motion -- 7.4.2 Some * continuous hypermodels of Brownian motion -- 7.4.3 Some examples -- 7.5 Itô Integral and Stochastic Differential Equations -- 7.5.1 Some general remarks -- 7.5.2 Wiener integral and Itô integral -- 7.5.3 Itô's lemma and the Stratonovitch integral -- 7.6 Solving Stochastic differential equations -- 7.7 Malliavin calculus -- 7.8 White noise analysis -- 7.9 Universality and homogeneity properties of hyperfinite models -- Appendix. Investments Mathematical models. http://id.loc.gov/authorities/subjects/sh85067718 Securities Mathematical models. Risk management Mathematical models. Investissements Modèles mathématiques. Gestion du risque Modèles mathématiques. BUSINESS & ECONOMICS Investments & Securities General. bisacsh Investments Mathematical models fast Risk management Mathematical models fast Securities Mathematical models fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85067718 |
| title | Hypermodels in mathematical finance : modelling via infinitesimal analysis / |
| title_auth | Hypermodels in mathematical finance : modelling via infinitesimal analysis / |
| title_exact_search | Hypermodels in mathematical finance : modelling via infinitesimal analysis / |
| title_full | Hypermodels in mathematical finance : modelling via infinitesimal analysis / Siu-Ah Ng. |
| title_fullStr | Hypermodels in mathematical finance : modelling via infinitesimal analysis / Siu-Ah Ng. |
| title_full_unstemmed | Hypermodels in mathematical finance : modelling via infinitesimal analysis / Siu-Ah Ng. |
| title_short | Hypermodels in mathematical finance : |
| title_sort | hypermodels in mathematical finance modelling via infinitesimal analysis |
| title_sub | modelling via infinitesimal analysis / |
| topic | Investments Mathematical models. http://id.loc.gov/authorities/subjects/sh85067718 Securities Mathematical models. Risk management Mathematical models. Investissements Modèles mathématiques. Gestion du risque Modèles mathématiques. BUSINESS & ECONOMICS Investments & Securities General. bisacsh Investments Mathematical models fast Risk management Mathematical models fast Securities Mathematical models fast |
| topic_facet | Investments Mathematical models. Securities Mathematical models. Risk management Mathematical models. Investissements Modèles mathématiques. Gestion du risque Modèles mathématiques. BUSINESS & ECONOMICS Investments & Securities General. Investments Mathematical models Risk management Mathematical models Securities Mathematical models |
| work_keys_str_mv | AT ngsiuah hypermodelsinmathematicalfinancemodellingviainfinitesimalanalysis |