Mathematics of financial obligations / A. V. Melʹnikov, S. N. Volkov, M. L. Nechaev.

Format:

Book

Author/Creator:

Melʹnikov, A. V., 1953-

Contributor:

Volkov, S. N. (Sergeĭ Nikolaevich), 1972-

Nechaev, M. L. (Mikhail Leonidovich), 1972-

Series:

Translations of mathematical monographs 0065-9282 ; v. 212.

Translations of mathematical monographs, 0065-9282 ; v. 212

Standardized Title:

Matematika finansovykh obi͡azatelʹstv. English

Language:

English

Russian

Subjects (All):

Investments--Mathematics.

Investments.

Stochastic analysis.

Hedging (Finance)--Mathematical models.

Hedging (Finance).

Insurance--Mathematics.

Insurance.

Physical Description:

ix, 194 pages : illustrations ; 26 cm.

Place of Publication:

Providence, R.I. : American Mathematical Society, [2002]

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.

Notes:

Includes bibliographical references (pages 185-190) and index.

ISBN:

0821829459

OCLC:

49952355