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Brownian Motion Calculus presents the basics of Stochastic Calculus with a focus on the valuation of financial derivatives. It is intended as an accessible introduction to the technical literature. A clear distinction has been made between the mathematics that is convenient for a first introduction, and the more rigorous underpinnings which are best studied from the selected technical references. The inclusion of fully worked out exercises makes the book attractive for self study. Standard probability theory and ordinary calculus are the prerequisites. Summary slides for revision and teaching can be found on the book website.…mehr

Produktbeschreibung
Brownian Motion Calculus presents the basics of Stochastic Calculus with a focus on the valuation of financial derivatives. It is intended as an accessible introduction to the technical literature. A clear distinction has been made between the mathematics that is convenient for a first introduction, and the more rigorous underpinnings which are best studied from the selected technical references. The inclusion of fully worked out exercises makes the book attractive for self study. Standard probability theory and ordinary calculus are the prerequisites. Summary slides for revision and teaching can be found on the book website.

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  • Produktdetails
  • Verlag: John Wiley & Sons
  • Seitenzahl: 330
  • Erscheinungstermin: 14.09.2008
  • Englisch
  • ISBN-13: 9780470021712
  • Artikelnr.: 37289843
Autorenporträt
UBBO WIERSEMA was educated in Applied Mathematics at Delft, in Operations Research at Berkeley, and in Financial Economics and Financial Mathematics at the London School of Economics. He joined The Business School for Financial Markets (the ICMA Centre) at the University of Reading, UK, in 1997, to develop and teach its curriculum in Quantitative Finance. Prior to that, he was a derivatives mathematician at the merchant bank Robert Fleming in the City of London. Before that his career was focused in Operations Research in the US and Europe.
Inhaltsangabe
1. Brownian Motion Origins Notion of a Random Process Brownian Motion Stock Price Dynamics Construction of Brownian Motion from a Discrete Symmetric Random Walk Features of Brownian Motion Paths Computations with Brownian motion References Examples 2. Martingales Introduction Filtration Conditional Expectation Martingale Martingale examples References Examples 3. Ito Stochastic Integration How a Stochastic integral arises in stock trading Construction of Ito Stochastic integral for random step functions Extension to general random integrands Summary of properties of an Ito stochastic integral Reference Examples 4. Ito Calculus Stochastic differential notation Taylor's expansion in ordinary calculus Ito's formula as a set of rules Illustrations of Ito's formula Justification of Ito's formula References Examples 5. Stochastic differential equations Structure of a stochastic differental equation Stocastic differntail equations arising in finance Finding a closed form solution Checking the solution of an sde General method for solving sde's References Examples 6. Risk
neutral probability Risk
neutral valuation
the basic concept Risk
neutral probability construction in discrete one period binomial framework Risk
neutral probability construction in the continuous framework Girsanov's theorem Radon
Nikodym derivative Numerical Illustration Motivation for Girsanov's theorem Summary References 7. Feynman
Kac Representation Stochastic Representation Derivation of simple Feynman
Kac formula Application to Black Scholes pde Generalisations Solution by Simulation References Annexes Computations with Brownian motion Riemann Integration Brownian Motion Variability Norms Einstrin's Model of Brownian Motion