Meyer Continuous Stochastic Calculus with Applications to Finance

Erscheinungsjahr 2002
ISBN: 978-1-4200-3559-9
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 336 Seiten

Reihe: Applied Mathematics

The prolonged boom in the US and European stock markets has led to increased interest in the mathematics of security markets, most notably in the theory of stochastic integration. This text gives a rigorous development of the theory of stochastic integration as it applies to the valuation of derivative securities. It includes all the tools necessary for readers to understand how the stochastic integral is constructed with respect to a general continuous martingale.

The author develops the stochastic calculus from first principles, but at a relaxed pace that includes proofs that are detailed, but streamlined to applications to finance. The treatment requires minimal prerequisites-a basic knowledge of measure theoretic probability and Hilbert space theory-and devotes an entire chapter to application in finances, including the Black Scholes market, pricing contingent claims, the general market model, pricing of random payoffs, and interest rate derivatives.

Continuous Stochastic Calculus with Application to Finance is your first opportunity to explore stochastic integration at a reasonable and practical mathematical level. It offers a treatment well balanced between aesthetic appeal, degree of generality, depth, and ease of reading.

Zielgruppe

Instructors and graduate students in mathematics and finance; Banker engaged in the trading of interest rate derivatives

Autoren/Hrsg.

Meyer, Michael

Fachgebiete

• Wirtschaftswissenschaften Volkswirtschaftslehre Volkswirtschaftslehre Allgemein
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Mathematik | Informatik Mathematik Stochastik Elementare Stochastik
• Mathematik | Informatik Mathematik Stochastik Stochastische Prozesse
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik

Inhaltsverzeichnis

MARTINGALE THEORY
Covergence of Random Variables
Conditioning
Submartingales
Convergence Theorems
Optional Sampling of Closed Submartingale Sequences
Maximal Inequalities for Submartingale Sequences
Continuous Time Martingales
Local Martingales
Quadratic Variation
The Covariation Process
Semimartingales
BROWNIAN MOTION
Gaussian Process
One Dimensional Brownian Motion
STOCHASTIC INTEGRATION
Measurability Properties of Stochastic Processes
Stochastic Integration with Respect to Continuous Semimartingales
Ito's Formula
Change of Measure
Representation of Continuous Local Martingales
Miscellaneous
APPLICATION TO FINANCE
The Simple Black Scholes Market
Pricing of Contingent Claims
The General Market Model
Pricing of Random Payoffs at Fixed Future Dates
Interest Rate Derivatives
APPENDIX
Separation of Convex Sets
The Basic Extension Procedure
Positive Semidefinite Matrices
Kolmogoroff Existence Theorem