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Author: David Nualart
Publisher: Cambridge University Press
Published: 2018-09-27
Total Pages: 249
ISBN-13: 1107039126
DOWNLOAD EBOOKA compact introduction to this active and powerful area of research, combining basic theory, core techniques, and recent applications.
Author: Giuseppe Da Prato
Publisher: Springer
Published: 2014-07-01
Total Pages: 286
ISBN-13: 8876424997
DOWNLOAD EBOOKThis volume presents an introductory course on differential stochastic equations and Malliavin calculus. The material of the book has grown out of a series of courses delivered at the Scuola Normale Superiore di Pisa (and also at the Trento and Funchal Universities) and has been refined over several years of teaching experience in the subject. The lectures are addressed to a reader who is familiar with basic notions of measure theory and functional analysis. The first part is devoted to the Gaussian measure in a separable Hilbert space, the Malliavin derivative, the construction of the Brownian motion and Itô's formula. The second part deals with differential stochastic equations and their connection with parabolic problems. The third part provides an introduction to the Malliavin calculus. Several applications are given, notably the Feynman-Kac, Girsanov and Clark-Ocone formulae, the Krylov-Bogoliubov and Von Neumann theorems. In this third edition several small improvements are added and a new section devoted to the differentiability of the Feynman-Kac semigroup is introduced. A considerable number of corrections and improvements have been made.
Author: Giulia Di Nunno
Publisher: Springer Science & Business Media
Published: 2008-10-08
Total Pages: 421
ISBN-13: 3540785728
DOWNLOAD EBOOKThis book is an introduction to Malliavin calculus as a generalization of the classical non-anticipating Ito calculus to an anticipating setting. It presents the development of the theory and its use in new fields of application.
Author: David Nualart
Publisher: Springer Science & Business Media
Published: 2013-12-11
Total Pages: 273
ISBN-13: 1475724373
DOWNLOAD EBOOKThe origin of this book lies in an invitation to give a series of lectures on Malliavin calculus at the Probability Seminar of Venezuela, in April 1985. The contents of these lectures were published in Spanish in [176]. Later these notes were completed and improved in two courses on Malliavin cal culus given at the University of California at Irvine in 1986 and at Ecole Polytechnique Federale de Lausanne in 1989. The contents of these courses correspond to the material presented in Chapters 1 and 2 of this book. Chapter 3 deals with the anticipating stochastic calculus and it was de veloped from our collaboration with Moshe Zakai and Etienne Pardoux. The series of lectures given at the Eighth Chilean Winter School in Prob ability and Statistics, at Santiago de Chile, in July 1989, allowed us to write a pedagogical approach to the anticipating calculus which is the basis of Chapter 3. Chapter 4 deals with the nonlinear transformations of the Wiener measure and their applications to the study of the Markov property for solutions to stochastic differential equations with boundary conditions.
Author: Elisa Alos
Publisher: CRC Press
Published: 2021-07-14
Total Pages: 350
ISBN-13: 1000403513
DOWNLOAD EBOOKMalliavin Calculus in Finance: Theory and Practice aims to introduce the study of stochastic volatility (SV) models via Malliavin Calculus. Malliavin calculus has had a profound impact on stochastic analysis. Originally motivated by the study of the existence of smooth densities of certain random variables, it has proved to be a useful tool in many other problems. In particular, it has found applications in quantitative finance, as in the computation of hedging strategies or the efficient estimation of the Greeks. The objective of this book is to offer a bridge between theory and practice. It shows that Malliavin calculus is an easy-to-apply tool that allows us to recover, unify, and generalize several previous results in the literature on stochastic volatility modeling related to the vanilla, the forward, and the VIX implied volatility surfaces. It can be applied to local, stochastic, and also to rough volatilities (driven by a fractional Brownian motion) leading to simple and explicit results. Features Intermediate-advanced level text on quantitative finance, oriented to practitioners with a basic background in stochastic analysis, which could also be useful for researchers and students in quantitative finance Includes examples on concrete models such as the Heston, the SABR and rough volatilities, as well as several numerical experiments and the corresponding Python scripts Covers applications on vanillas, forward start options, and options on the VIX. The book also has a Github repository with the Python library corresponding to the numerical examples in the text. The library has been implemented so that the users can re-use the numerical code for building their examples. The repository can be accessed here: https://bit.ly/2KNex2Y.
Author: David Nualart
Publisher: American Mathematical Soc.
Published: 2009
Total Pages: 99
ISBN-13: 0821847791
DOWNLOAD EBOOKThe Malliavin calculus was developed to provide a probabilistic proof of Hormander's hypoellipticity theorem. The theory has expanded to encompass other significant applications. The main application of the Malliavin calculus is to establish the regularity of the probability distribution of functionals of an underlying Gaussian process. In this way, one can prove the existence and smoothness of the density for solutions of various stochastic differential equations. More recently, applications of the Malliavin calculus in areas such as stochastic calculus for fractional Brownian motion, central limit theorems for multiple stochastic integrals, and mathematical finance have emerged. The first part of the book covers the basic results of the Malliavin calculus. The middle part establishes the existence and smoothness results that then lead to the proof of Hormander's hypoellipticity theorem. The last part discusses the recent developments for Brownian motion, central limit theorems, and mathematical finance.
Author: Denis R. Bell
Publisher: Courier Corporation
Published: 2012-12-03
Total Pages: 124
ISBN-13: 0486152057
DOWNLOAD EBOOKThis introductory text presents detailed accounts of the different forms of the theory developed by Stroock and Bismut, discussions of the relationship between these two approaches, and a variety of applications. 1987 edition.
Author: Paul Malliavin
Publisher: Springer Science & Business Media
Published: 2006-02-25
Total Pages: 148
ISBN-13: 3540307990
DOWNLOAD EBOOKHighly esteemed author Topics covered are relevant and timely
Author: Ivan Nourdin
Publisher: Cambridge University Press
Published: 2012-05-10
Total Pages: 255
ISBN-13: 1107017777
DOWNLOAD EBOOKThis book shows how quantitative central limit theorems can be deduced by combining two powerful probabilistic techniques: Stein's method and Malliavin calculus.
Author: Hiroyuki Matsumoto
Publisher: Cambridge University Press
Published: 2017
Total Pages: 359
ISBN-13: 110714051X
DOWNLOAD EBOOKDeveloping the Itô calculus and Malliavin calculus in tandem, this book crystallizes modern day stochastic analysis into a single volume.
