Continuous Stochastic Calculus with Applications to Finance: 1st Edition (Hardback) book cover

Continuous Stochastic Calculus with Applications to Finance

1st Edition

By Michael Meyer

Chapman and Hall/CRC

336 pages | 20 B/W Illus.

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Hardback: 9781584882343
pub: 2000-10-25
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Description

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.

Reviews

"As a reference or a second book on stochastic calculus, Meyer is outstanding. In a formal, highly rigorous manner, he develops stochastic calculus, all the while focusing on topics of primary interest to financial engineers. … I highly recommend Meyer. It is an excellent introduction and reference on stochastic calculus."

- Glyn A. Holton of Contingency Analysis

Table of Contents

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

About the Series

Applied Mathematics

Learn more…

Subject Categories

BISAC Subject Codes/Headings:
BUS027000
BUSINESS & ECONOMICS / Finance
MAT000000
MATHEMATICS / General
MAT003000
MATHEMATICS / Applied