Introduction to
Stochastic Calculus for Finance
A New Didactic Approach
This short book introduces stochastic
calculus with applications in finance. It adopts a new approach to
explaining stochastic calculus first proposed by Follmer. This downplays
probability and emphasizes paths of stochastic processes as continuous
functions of unbounded variation. The book will appeal to
experts interested in this new approach ...
Stochastic Calculus of Variations in Mathematical
Finance
Paul Malliavin and Anton Thalmaier
2005
Author Paul
Malliavin is being modest. What he chooses to call stochastic calculus of
variations is more commonly called Malliavin calculus. He launched the field in
1974, when he used it in prove a result in stochastic calculus. It has
since found applications in a number of fields, including finance, where
the ability to perform integration by parts facilitates direct
calculation of the Greeks ...
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Introduction to Stochastic Calculus
with Applications
Fima C. Klebaner
2005
A formal understanding
of stochastic calculus requires knowledge of measure theory and
measure-theoretic probability. Because these prerequisites are
significant, there is considerable demand for books that can communicate
a working knowledge of stochastic calculus to readers unfamiliar with
measure theory ....
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Stochastic Differential Equations
Bernt Oksendal
2003
Among financial
engineers, Oksendal is one of the most popular stochastic calculus texts. This
is partly due to its pedigree. First published in 1985, it is now in its sixth
edition—so it has had plenty of time to establish itself. It is more advanced
than the competing classic by Malliaris and Brock (1982) ...
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Stochastic Calculus and Financial Applications
Michael Steele
2001
Steele's book is a
sophisticated introduction to stochastic calculus with applications from
basic Black-Scholes theory. There are other financially oriented
introductions to stochastic calculus. What sets this one apart is its
sophistication. Steele assumes a strong working knowledge of measure
theory and a passing familiarity with function spaces ...
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Continuous Stochastic Calculus
with Applications to Finance
Michael Meyer
2000
For mathematically
sophisticated readers, Meyer is an excellent text on stochastic calculus with
applications to finance. It is at a technical level comparable to Oksendal (2003).
It differs from that book in that ...
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Brownian Motion and Stochastic Calculus
I. Karatzas and S. Shreve
1991
Karatzas and
Shreve is well known to financial engineers. It is a very advanced text on
stochastic calculus. The authors claim to, in some areas, take readers to the
cutting edge of current research. I am not a researcher in the field, so I cannot
speak to this claim. However, based on the sophistication of the discourse, I
don't doubt it. ... Read more
Kiyosi Ito: Selected Papers
Daniel Stroock and S.R.S. Varadhan
(eds.)
1987
Kiyosi Ito is a giant of stochastic calculus. He
published in Japanese journals, and sometimes in Japanese. This made his
works inaccessible to many researchers. That is what makes this volume
such a godsend. It is an edited collection of his seminal works, with
translations where necessary. There is excellent introductory material,
a foreword by Ito, and a biography of Ito. It is an essential volume for
serious students of stochastic calculus ...
Stochastic Methods in Economics and Finance
A. G. Malliaris and W. A. Brock
1982
Malliaris and Brock is
a classic of financial engineering. During the formative days of the OTC
derivatives markets, it was from this book that early financial
engineers learned stochastic calculus. It remains an excellent book
today ... Read more
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Fima C. Klebaner
Bernt Oksendal
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