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Author : Paul Malliavin
Release : 2006-02-25
Genre : Business & Economics
Kind : eBook
Book Rating : 990/5 ( reviews)
Book Synopsis Stochastic Calculus of Variations in Mathematical Finance by : Paul Malliavin
Download or read book Stochastic Calculus of Variations in Mathematical Finance written by Paul Malliavin. This book was released on 2006-02-25. Available in PDF, EPUB and Kindle. Book excerpt: Highly esteemed author Topics covered are relevant and timely
Author : Yasushi Ishikawa
Release : 2023-07-24
Genre : Mathematics
Kind : eBook
Book Rating : 293/5 ( reviews)
Book Synopsis Stochastic Calculus of Variations by : Yasushi Ishikawa
Download or read book Stochastic Calculus of Variations written by Yasushi Ishikawa. This book was released on 2023-07-24. Available in PDF, EPUB and Kindle. Book excerpt: This book is a concise introduction to the stochastic calculus of variations for processes with jumps. The author provides many results on this topic in a self-contained way for e.g., stochastic differential equations (SDEs) with jumps. The book also contains some applications of the stochastic calculus for processes with jumps to the control theory, mathematical finance and so. This third and entirely revised edition of the work is updated to reflect the latest developments in the theory and some applications with graphics.
Author : Yasushi Ishikawa
Release : 2016-03-07
Genre : Mathematics
Kind : eBook
Book Rating : 321/5 ( reviews)
Book Synopsis Stochastic Calculus of Variations by : Yasushi Ishikawa
Download or read book Stochastic Calculus of Variations written by Yasushi Ishikawa. This book was released on 2016-03-07. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is a concise introduction to the stochastic calculus of variations (also known as Malliavin calculus) for processes with jumps. It is written for researchers and graduate students who are interested in Malliavin calculus for jump processes. In this book "processes with jumps" includes both pure jump processes and jump-diffusions. The author provides many results on this topic in a self-contained way; this also applies to stochastic differential equations (SDEs) "with jumps". The book also contains some applications of the stochastic calculus for processes with jumps to the control theory and mathematical finance. Namely, asymptotic expansions functionals related with financial assets of jump-diffusion are provided based on the theory of asymptotic expansion on the Wiener–Poisson space. Solving the Hamilton–Jacobi–Bellman (HJB) equation of integro-differential type is related with solving the classical Merton problem and the Ramsey theory. The field of jump processes is nowadays quite wide-ranging, from the Lévy processes to SDEs with jumps. Recent developments in stochastic analysis have enabled us to express various results in a compact form. Up to now, these topics were rarely discussed in a monograph. Contents: Preface Preface to the second edition Introduction Lévy processes and Itô calculus Perturbations and properties of the probability law Analysis of Wiener–Poisson functionals Applications Appendix Bibliography List of symbols Index
Author : Ciprian Tudor
Release : 2013-08-13
Genre : Mathematics
Kind : eBook
Book Rating : 362/5 ( reviews)
Book Synopsis Analysis of Variations for Self-similar Processes by : Ciprian Tudor
Download or read book Analysis of Variations for Self-similar Processes written by Ciprian Tudor. This book was released on 2013-08-13. Available in PDF, EPUB and Kindle. Book excerpt: Self-similar processes are stochastic processes that are invariant in distribution under suitable time scaling, and are a subject intensively studied in the last few decades. This book presents the basic properties of these processes and focuses on the study of their variation using stochastic analysis. While self-similar processes, and especially fractional Brownian motion, have been discussed in several books, some new classes have recently emerged in the scientific literature. Some of them are extensions of fractional Brownian motion (bifractional Brownian motion, subtractional Brownian motion, Hermite processes), while others are solutions to the partial differential equations driven by fractional noises. In this monograph the author discusses the basic properties of these new classes of self-similar processes and their interrelationship. At the same time a new approach (based on stochastic calculus, especially Malliavin calculus) to studying the behavior of the variations of self-similar processes has been developed over the last decade. This work surveys these recent techniques and findings on limit theorems and Malliavin calculus.
Author : Frederi Viens
Release : 2013-02-15
Genre : Mathematics
Kind : eBook
Book Rating : 060/5 ( reviews)
Book Synopsis Malliavin Calculus and Stochastic Analysis by : Frederi Viens
Download or read book Malliavin Calculus and Stochastic Analysis written by Frederi Viens. This book was released on 2013-02-15. Available in PDF, EPUB and Kindle. Book excerpt: The stochastic calculus of variations of Paul Malliavin (1925 - 2010), known today as the Malliavin Calculus, has found many applications, within and beyond the core mathematical discipline. Stochastic analysis provides a fruitful interpretation of this calculus, particularly as described by David Nualart and the scores of mathematicians he influences and with whom he collaborates. Many of these, including leading stochastic analysts and junior researchers, presented their cutting-edge research at an international conference in honor of David Nualart's career, on March 19-21, 2011, at the University of Kansas, USA. These scholars and other top-level mathematicians have kindly contributed research articles for this refereed volume.
