Malliavin-skorohod Calculus for Additive Processes With Applications to Finance PDF Download

Author: Josep Vives Santa-eulalia
Publisher: Chapman & Hall/CRC
ISBN: 9781498768559
Category :
Languages : en
Pages : 400

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Author: Giulia Di Nunno
Publisher: Springer Science & Business Media
ISBN: 3540785728
Category : Mathematics
Languages : en
Pages : 421

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Book Description
This 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: Giulia Di Nunno
Publisher:
ISBN: 9781282631724
Category : Lévy processes
Languages : en
Pages : 413

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Book 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.

Author: David Nualart
Publisher: American Mathematical Soc.
ISBN: 0821883372
Category : Mathematics
Languages : en
Pages : 99

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Book Description
The derivative operator The divergence operator The Ornstein-Uhlenbeck semigroup Sobolev spaces and equivalence of norms Regularity of probability laws Support properties. Density of the maximum Application of Malliavin calculus to diffusion processes The divergence operator as a stochastic integral Central limit theorems and Malliavin calculus Applications of Malliavin calculus in finance Bibliography Index

Author: Paul Malliavin
Publisher: Springer Science & Business Media
ISBN: 3540307990
Category : Business & Economics
Languages : en
Pages : 148

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Highly esteemed author Topics covered are relevant and timely

Author: Elisa Alos
Publisher: CRC Press
ISBN: 1000403513
Category : Mathematics
Languages : en
Pages : 350

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Book Description
Malliavin 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: Julia Di Nunno
Publisher: Springer Science & Business Media
ISBN: 364218412X
Category : Mathematics
Languages : en
Pages : 532

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Book Description
This book presents innovations in the mathematical foundations of financial analysis and numerical methods for finance and applications to the modeling of risk. The topics selected include measures of risk, credit contagion, insider trading, information in finance, stochastic control and its applications to portfolio choices and liquidation, models of liquidity, pricing, and hedging. The models presented are based on the use of Brownian motion, Lévy processes and jump diffusions. Moreover, fractional Brownian motion and ambit processes are also introduced at various levels. The chosen blend of topics gives an overview of the frontiers of mathematics for finance. New results, new methods and new models are all introduced in different forms according to the subject. Additionally, the existing literature on the topic is reviewed. The diversity of the topics makes the book suitable for graduate students, researchers and practitioners in the areas of financial modeling and quantitative finance. The chapters will also be of interest to experts in the financial market interested in new methods and products. This volume presents the results of the European ESF research networking program Advanced Mathematical Methods for Finance.

Author: David Nualart
Publisher: Cambridge University Press
ISBN: 1107039126
Category : Business & Economics
Languages : en
Pages : 249

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Book Description
A compact introduction to this active and powerful area of research, combining basic theory, core techniques, and recent applications.

Author: Ole E. Barndorff-Nielsen
Publisher: Springer
ISBN: 3319941291
Category : Mathematics
Languages : en
Pages : 402

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Book Description
Drawing on advanced probability theory, Ambit Stochastics is used to model stochastic processes which depend on both time and space. This monograph, the first on the subject, provides a reference for this burgeoning field, complete with the applications that have driven its development. Unique to Ambit Stochastics are ambit sets, which allow the delimitation of space-time to a zone of interest, and ambit fields, which are particularly well-adapted to modelling stochastic volatility or intermittency. These attributes lend themselves notably to applications in the statistical theory of turbulence and financial econometrics. In addition to the theory and applications of Ambit Stochastics, the book also contains new theory on the simulation of ambit fields and a comprehensive stochastic integration theory for Volterra processes in a non-semimartingale context. Written by pioneers in the subject, this book will appeal to researchers and graduate students interested in empirical stochastic modelling.

Author: Hansjörg Albrecher
Publisher: Walter de Gruyter
ISBN: 3110213141
Category : Mathematics
Languages : en
Pages : 465

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Book Description
This book is a collection of state–of–the–art surveys on various topics in mathematical finance, with an emphasis on recent modelling and computational approaches. The volume is related to a 'Special Semester on Stochastics with Emphasis on Finance' that took place from September to December 2008 at the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences in Linz, Austria.