Continuous stochastic calculus with applications to finance

Michael Meyer1584882344, 9781584882343, 9781420035599

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.

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Table of contents :
PREFACE……Page 6
TABLE OF CONTENTS……Page 10
SUMMARY OF NOTATION……Page 14
1 Martingale Theory……Page 18
2 Brownian Motion……Page 120
3 Stochastic Integration……Page 148
4 Application to Finance……Page 228
APPENDIX……Page 314
BIBLIOGRAPHY……Page 330
INDEX……Page 332