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- [Browse]
Uniform title
Format
Book
Language
English
Published/​Created
Providence, R.I. : American Mathematical Society, ©2002.
Description
ix, 194 pages : illustrations ; 26 cm.

Availability

Copies in the Library

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Lewis Library - Stacks HG4515.3 .M4513 2002 Browse related items Request

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    Subject(s)
    Series
    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.
    ISBN
    • 0821829459 ((alk. paper))
    • 9780821829455 ((alk. paper))
    LCCN
    2002074395
    OCLC
    49952355
    Other standard number
    • 40008409386
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