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American Mathematical Society
Mathematics of Financial Obligations / Edition 1

Mathematics of Financial Obligations / Edition 1


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Product Details

ISBN-13: 9780821829455
Publisher: American Mathematical Society
Publication date: 07/01/2002
Series: Translations of Mathematical Monographs , #212
Edition description: New Edition
Pages: 194
Product dimensions: 7.20(w) x 10.20(h) x 0.60(d)

Table of Contents

Main Notationix
Chapter 1.Financial Systems: Innovations and the Risk Calculus1
1.1.Financial systems and their innovation changes1
1.2.General statements in the analysis of contingent claims. Models, methods, facts3
1.3.Dynamics of financial markets: from incomplete markets to complete markets through financial innovations10
1.4.Financial innovations and insurance risks13
Chapter 2.Random Processes and the Stochastic Calculus17
2.1.Random processes and their distributions. The Wiener process17
2.2.Diffusion processes. The Kolmogorov-Ito formula, Girsanov's theorem, representations of martingales20
2.3.Semimartingales and the stochastic calculus25
Chapter 3.Hedging and Investment in Complete Markets31
3.1.A martingale characterization of strategies and perfect hedging31
3.2.A methodology for finding martingale measures and pricing contingent claims for different models of a (B, S)-market34
3.3.A methodology for optimal investment and its applications43
Chapter 4.Hedging and Incomplete Markets49
4.1.A methodology for superhedging49
4.2.The Black-Scholes model with stochastic volatility52
4.3.Estimation of volatility61
Chapter 5.Markets with Structural Constraints and Transaction Costs65
5.1.Calculations in models of markets with structural constraints: A general methodology and its concrete realization65
5.2.Hedging and investment with transaction costs87
5.3.Appendix: Examples of the simulation of hedging strategies92
Chapter 6.Imperfect Forms of Hedging97
6.1.Mean-variance hedging97
6.2.Quantile hedging104
Chapter 7.Dynamic Contingent Claims and American Options121
7.1.Pricing dynamic contingent claims and the optimal stopping problem121
7.2.Concretization of option calculations and closed analytic formulas for prices and strategies126
7.3.Quantile hedging of dynamic contingent claims132
Chapter 8.Analysis of "Bond" Contingent Claims139
8.1.Models of the term structure of interest rates139
8.2.Hedging on a bond market144
8.3.Investing in a bond market153
Chapter 9.Economics of Insurance and Finance: Convergence of Quantitative Methods of Calculations159
9.1."Non-life" insurance. Traditional actuarial principles for calculating premiums and the financial no-arbitrage principle in a model of collective risk159
9.2.Life insurance. Mortality tables. Calculation of premiums and reserves in traditional and innovation insurance schemes167
9.3.Estimation of the ruin probability171
9.4.Catastrophe risks and reinsurance of them on financial markets176
Bibliographical Notes181
Subject Index191

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