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Mathematics of financial obligations / A.V. Melʹnikov, S.N. Volkov, M.L. Nechaev ; [translated from the Russian by H.H. McFaden].
Author
Melʹnikov, A. V., 1953-
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Uniform title
Matematika finansovykh obi︠a︡zatelʹstv.
English
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Format
Book
Language
English
Published/Created
Providence, R.I. : American Mathematical Society, ©2002.
Description
ix, 194 pages : illustrations ; 26 cm.
Availability
Available Online
Translations of mathematical monographs 1962-2012
Copies in the Library
Location
Call Number
Status
Location Service
Notes
Lewis Library - Stacks
HG4515.3 .M4513 2002
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Details
Subject(s)
Investments
—
Mathematics
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Stochastic analysis
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Hedging (Finance)
—
Mathematical models
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Insurance
—
Mathematics
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Related name
Volkov, S. N. (Sergeĭ Nikolaevich), 1972-
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Nechaev, M. L. (Mikhail Leonidovich), 1972-
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Series
Translations of mathematical monographs ; v. 212.
[More in this series]
Translations of mathematical monographs, 0065-9282 ; v. 212
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Summary note
"The book is geared toward specialists in finance and actuarial mathematics, practitioners in the financial and insurance business, students, and post-docs in corresponding areas of study. Readers should have a foundation in probability theory, random processes, and mathematical statistics."--Jacket.
Bibliographic references
Includes bibliographical references (p. 181-190) and index.
Contents
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 complete 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 theorem, 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 contingent claims for different models of a (B, S)-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
7.1. Pricing dynamic contingent claims and the optimal stopping problem 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 Quantitative Methods of Calculations 159
9.1. "Non-life" insurance. Traditional actuarial principles for calculating 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.
Show 34 more Contents items
ISBN
0821829459 ((alk. paper))
9780821829455 ((alk. paper))
LCCN
2002074395
OCLC
49952355
Other standard number
40008409386
Statement on language in description
Princeton University Library aims to describe library materials in a manner that is respectful to the individuals and communities who create, use, and are represented in the collections we manage.
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Mathematics of financial obligations / A. V. Mel'nikov, S. N. Volkov, M. L. Nechaev ; translated from the Russian by H. H. McFaden.
id
99125157366306421
Mathematics of financial obligations / A.V. Melʹnikov, S.N. Volkov, M.L. Nechaev.
id
SCSB-8714517