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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].
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BL
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| Record Number
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587059
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| Doc. No
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b416278
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| Uniform Title
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Matematika finansovykh obi͡azatelʹstv.English
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| Main Entry
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Melʹnikov, A. V.,1953-
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| Title & Author
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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].
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| Publication Statement
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Providence, R.I. :: American Mathematical Society,, c2002.
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| Series Statement
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Translations of mathematical monographs,; v. 212
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| Page. NO
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ix, 194 p. :: ill. ;; 26 cm.
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| ISBN
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0821829459 (alk. paper)
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: 9780821829455 (alk. paper)
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| Bibliographies/Indexes
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Includes bibliographical references (p. [185]-190) and index.
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| Contents
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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.
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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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| LC Classification
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HG4515.3.M4513 2002
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| Added Entry
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Volkov, S. N., (Sergeĭ Nikolaevich),1972-
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Nechaev, M. L., (Mikhail Leonidovich),1972-
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