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Elementary stochastic calculus with finance in view | |||||
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Autor: Mikosch, Thomas
Hodnocení: AnotaceModelling with the Itô 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 Itô calculus and/or stochastic finance. Contents: Preliminaries: Basic Concepts from Probability Theory; Stochastic Processes; Brownian Motion; Conditional Expectation; Martingales; The Stochastic Integral: The Riemann and Riemann Stieltjes Integrals; The Itô Integral; The Itô Lemma; The Stratonovich and Other Integrals; Stochastic Differential Equations: Deterministic Differential Equations; Itô 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; Appendices: 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. Dostupné zdroje
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