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- Product code: 13163
- ISBN: 9810235437,
ISBN13: 9789810235437,
224 pages, hardback
Published by World Scientific Books on 1998
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Description of Elementary Stochastic Calculus - with Finance in View |
Modelling with the It™ integral or stochastic differential equations has become increasingly important in various applied fields, including physics, biology, chemistry and finance. However, stochastic calculus is based on a deep mathematical theory.
This book is suitable for the reader without a deep mathematical background. It gives an elementary introduction to that area of probability theory, without burdening the reader with a great deal of measure theory.
Applications are taken from stochastic finance. In particular, the Black-Scholes option pricing formula is derived. The book can serve as a text for a course on stochastic calculus for non-mathematicians or as elementary reading material for anyone who wants to learn about It™ calculus and/or stochastic finance.
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Reviews"... this is a well written book, which makes the difficult object of mathematical finance easy to understand also for non-mathematicians. It might be useful for economics students and all practitioners in the field of finance who are interested in the mathematical methodology behind the Black-Scholes model."
- Statistical Papers, 2000
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Contents of Elementary Stochastic Calculus - with Finance in View |
Preliminaries: Basic Concepts from Probability Theory
- Stochastic Processes
- Brownian Motion
- Conditional Expectation
- Martingales
- The Stochastic Integral: The Riemann and Riemann-Stieltjes Integrals
-The It™ Integral
- The It™ Lemma
- The Stratonovich and Other Integrals
- Stochastic Differential Equations: Deterministic Differential Equations
- It™ Stochastic Differential Equations
- The General Linear Differential Equation
- Numerical Solution
- Applications of Stochastic Calculus in Finance: The Black-Scholes Option-Pricing Formula
- A Useful Technique: Change of Measure
Appendix: Modes of Convergence
- Inequalities
- Non-Differentiability and Unbounded Variation of Brownian Sample Paths
- Proof of the Existence of the General Itô Stochastic Integral
- The Radon–Nikodym Theorem
- Proof of the Existence and Uniqueness of the Conditional Expectation
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