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- Product code: 9671
- ISBN: 1557869456,
ISBN13: 9781557869456,
272 pages, hardback
Published by Blackwell Publishers on 1997
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Description of Introduction to Mathematical Finance |
This book is designed to serve as a textbook for advanced undergraduate and beginning graduate students who seek a rigorous yet accessible introduction to the modern financial theory of security markets. This is a subject that is taught in both business schools and mathematical science departments. The full theory of security markets requires knowledge of continuous time stochastic process models, measure theory, mathematical economics, and similar prerequisites which are generally not learned before the advanced graduate level. Hence a proper study of the full theory of security markets requires several years of graduate study. However, by restricting attention to discrete time models of security prices it is possible to acquire mathematics. In particular, while living in a discrete time world it is possible to learn virtually all of the important financial concepts. The purpose of this book is to provide such an introductory study.There is still a lot of mathematics in this book. The reader should be comfortable with calculus, linear algebra, and probability theory that is based on calculus, (but not necessarily measure theory).
Random variables and expected values will be playing important roles. The book will develop important notions concerning discrete time stochastic processes: prior knowledge here will be useful but is not required. Presumably the reader will be interested in finance and thus will come with some rudimentary knowledge of stocks, bonds, options, and financial decision making. The last topic involves utility theory, of course: hopefully the reader will be familiar with this and related topics of introductory microeconomic theory. Some exposure to linear programming would be advantageous, but not necessary.The aim of this book is to provide a rigorous treatment of the financial theory while maintaining a casual style. Readers seeking institutional knowledge about securities, derivatives, and portfolio management should look elsewhere, but those seeking a careful introduction to financial engineering will find that this is a useful and comprehensive introduction to the subject.
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Contents of Introduction to Mathematical Finance |
Preface
Acknowledgements
1. Single Period Securities Market
Model specifications
Arbitrage and other economic consideration
Risk neutral probability measures
Valuation of contingent claims
Complete and incomplete markets
Risk and return
2. Single Period Consumption and Investment
Optimal portfolios and viability
Risk neutral computational approach
Consumption investment problems
Mean-variance portfolio analysis
Portfolio management with short sales restrictions and similar constraints
Optimal portfolios in incomplete markets
Equilibrium models
3. Multiperiod Securities Markets
Model specifications, filtrations, and stochastic processes
Return and dividend processes
Conditional expectation and Martingales
Economic considerations
The Binomial model
Markov models
4. Options, Futures, and other Derivatives
Contingent claims
European options under the binomial model
American options
Complete and incomplete markets
Forward prices and cash stream valuation
Futures
5. Optimal Consumption and Investment Problems
Optimal portfolios and dynamic programming
Optimal portfolios and Martingale methods
Consumption-investment and dynamic programming
Consumption-investment and Martingale methods
Maximum utility from consumption and terminal wealth
Optimal portfolios with constraints
Optimal consumption-investment with constraints
Portfolio optimization in incomplete markets
6. Bonds and Interest Rate Derivatives
The basic term structure model
Lattice, Markov chain models
Yield curve models
Forward risk adjusted probability measures
Coupon bonds and bond options
Swaps and swaptions
Caps and floors
7. Models with Infinite Sample Spaces
Finite horizon models
Infinite Horizon Models
Appendix: Linear Programming
Bibliography
Index
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About S.R. Pliska |
Stanley Pliska is the founding editor of the scholarly journal Mathematical Finance. He is noted for his fundamental research on the mathematical and economic theory of security prices, especially his development of important bridges between stochastic calculus and arbitrage pricing theory as well as his discovery of the risk neutral computational approach for portfolio optimization problems. He is currently teaching and researching in the areas of interest rate derivatives and dynamic asset allocation.
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