Stochastic Calculus of Variations in Mathematical Finance

Gaussian Stochastic Calculus of Variations.- Pathwise propagation of Greeks in complete elliptic markets.- Market equilibrium and price-volatility feedback rate.-Multivariate conditioning and regularity of laws.- Non-elliptic markets and instability in HJM models.- Insider trading.- Rates of weak convergence and distribution theory on Gaussian spaces.-Fourier series method for the measurement of historical volatilities.

From the reviews:

"This short book introduces Malliavin calculus and illustrates important applications in finance. ... For readers with the necessary mathematical skills, this is a valuable introduction to the mathematics and financial applications of Malliavin calculus. ... it provides a direct gateway to the relevant literature." (www.riskbook.com, November, 2006)

"The book under review is on the applications of the Malliavin calculus to financial mathematics. ... The authors have written a short book introducing the reader efficiently to the key points of the Malliavin calculus in mathematical finance. ... Also the list of references is comprehensive and updated, and gives a clear picture of the activity and relevance of this approach to many financial problems. ... This book is recommended to all researchers in mathematical finance." (MathSciNet, February, 2007)

"The book under review is on the applications of the Malliavin calculus to financial mathematics. ... The compact form is to the advantage of the reader, who is led to the applications rather quickly. ... This book is recommended to all researchers in mathematical finance. It shows how advanced mathematics can play an important role in solving practical financial problems as well as developing new understanding and concepts." (Fred Espen Benth, Mathematical Reviews, Issue 2007 b)

"The book under review demonstrates the power and versatility of the Malliavin calculus in a variety of problems arising in Mathematical Finance. Despite being mathematically demanding, it is directed not only towards researchers in mathematics, but also to practitioners ... . The book will certainly address in the first place researchers in mathematical finance. It can however be recommended to a much wider public in mathematics beyond probability ... ." (Peter Imkeller, Zentralblatt MATH, Vol. 1124 (1), 2008)

"This monograph is devoted to an updated presentation, in a rigorous mathematical framework, of the applications of the stochastic calculus of variations in mathematical finance. ... In conclusion, this book aims to explain the role played by the stochastic calculus of variations in mathematical finance, and it will be useful for researchers working in these fields." (David Nualart, Bulletin of the American Mathematical Society, Vol. 44 (3), July, 2007)