Malliavin Calculus for Lévy Processes with Applications to Finance (Universitext) |  | Authors: Giulia Di Nunno, Bernt Øksendal, Frank Proske
Publisher: Springer
List Price: $59.95
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Rating:  1 reviews
Sales Rank: 103240
Media: Paperback
Edition: 1st ed. 2009. Corr. 2nd printing
Pages: 417
Number Of Items: 1
Shipping Weight (lbs): 1.5
Dimensions (in): 9.3 x 6.1 x 1
ISBN: 354078571X
Dewey Decimal Number: 515
EAN: 9783540785712
ASIN: 354078571X
Publication Date: October 1, 2009
Availability: Usually ships in 1-2 business days
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Product Description
While the original works on Malliavin calculus aimed to study the smoothness of densities of solutions to stochastic differential equations, this book has another goal. It portrays the most important and innovative applications in stochastic control and finance, such as hedging in complete and incomplete markets, optimisation in the presence of asymmetric information and also pricing and sensitivity analysis. In a self-contained fashion, both the Malliavin calculus with respect to Brownian motion and general Lévy type of noise are treated. Besides, forward integration is included and indeed extended to general Lévy processes. The forward integration is a recent development within anticipative stochastic calculus that, together with the Malliavin calculus, provides new methods for the study of insider trading problems. To allow more flexibility in the treatment of the mathematical tools, the generalization of Malliavin calculus to the white noise framework is also discussed. This book is a valuable resource for graduate students, lecturers in stochastic analysis and applied researchers.
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| Customer Reviews:
Theoretical framework December 18, 2008
Bachelier (Ile de France)
1 out of 4 found this review helpful
Malliavin calculus was started for fluid dynamics and densities of solutions and stochastic differential equations that described them (okay, here is a hint...imagine water, that is a fluid with a certain density, and it moves through *rocks* which are also fluid (just a very very slow moving fluid) and also have a different density. Malvian calculus describes all that).
Malliavin Calculus for Lévy Processes with Applications to Finance takes the insights worked out in fluid mechanics engineering and applies them to finance.
Emphasis is on stochastic control and finance and regime switching. Topics include hedging in complete and incomplete markets, optimization, optimization with asymmetric information, and also price sensitivity analysis with asymmetric information and steep of flat utility curves. All this using Malliavin calculus, Brownian motion and general Bachelier (Levy-Einstein) noise environments.
Forward integration is extended to general Bachelier processes and insider trading (again, asymmetric information) analysis.
The book is for math grad students and researchers in this specialized field. About half of these essays are marginally useful for practitioners, but most is set in a theoretical framework world.
Throughout the work Bachelier processes are mis-named "Levy processes." An insult to the late Louis Bachelier and an undeserved continuation of recognition for Levy in the field which he does not deserve (keep in mind Levy did make many contributions to the field, just that Brownian motion was first applied by Bachelier and only latter expanded on by Levy, ironically at physics problems and not on finance ones, whereas Bachelier had the insight that finance problems was the most fruitful area of inquiry).
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