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|a Ng, Siu-Ah.
|0 http://id.loc.gov/authorities/names/no2003055658
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| 245 |
1 |
0 |
|a Hypermodels in mathematical finance :
|b modelling via infinitesimal analysis /
|c Siu-Ah Ng.
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| 260 |
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|a River Edge, N.J. :
|b World Scientific,
|c ©2003.
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| 300 |
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|a 1 online resource (xiii, 298 pages) :
|b illustrations
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| 336 |
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|a text
|b txt
|2 rdacontent
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|a computer
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|a Includes bibliographical references (pages 289-294) and index.
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|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.
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|a Print version record.
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| 520 |
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|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.
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| 546 |
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|a English.
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| 650 |
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0 |
|a Investments
|x Mathematical models.
|0 http://id.loc.gov/authorities/subjects/sh85067718
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| 650 |
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0 |
|a Securities
|x Mathematical models.
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| 650 |
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|a Risk management
|x Mathematical models.
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| 650 |
|
7 |
|a BUSINESS & ECONOMICS
|x Investments & Securities
|x General.
|2 bisacsh
|
| 650 |
|
7 |
|a Investments
|x Mathematical models.
|2 fast
|0 (OCoLC)fst00978277
|
| 650 |
|
7 |
|a Risk management
|x Mathematical models.
|2 fast
|0 (OCoLC)fst01098179
|
| 650 |
|
7 |
|a Securities
|x Mathematical models.
|2 fast
|0 (OCoLC)fst01110768
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| 655 |
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|a Electronic books.
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| 655 |
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4 |
|a Electronic books.
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|i Print version:
|a Ng, Siu-Ah.
|t Hypermodels in mathematical finance.
|d River Edge, N.J. : World Scientific, ©2003
|w (DLC) 52066471
|
| 903 |
|
|
|a HeVa
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| 929 |
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|t Library of Congress classification
|a HG4515.2 .N4 2003eb
|l Online
|c UC-FullText
|u https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=e000xna&AN=134085
|z eBooks on EBSCOhost
|g ebooks
|i 12248339
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