Malliavin Calculus For L Vy Processes With Applications To Finance
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Malliavin Calculus For L Vy Processes With Applications To Finance
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Author : Giulia Di Nunno
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-10-08
Malliavin Calculus For L Vy Processes With Applications To Finance written by Giulia Di Nunno and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-10-08 with Mathematics categories.
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.
Let Us Use White Noise
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Author : Takeyuki Hida
language : en
Publisher: World Scientific
Release Date : 2017-03-10
Let Us Use White Noise written by Takeyuki Hida and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-10 with Mathematics categories.
Why should we use white noise analysis? Well, one reason of course is that it fills that earlier gap in the tool kit. As Hida would put it, white noise provides us with a useful set of independent coordinates, parametrized by 'time'. And there is a feature which makes white noise analysis extremely user-friendly. Typically the physicist — and not only he — sits there with some heuristic ansatz, like e.g. the famous Feynman 'integral', wondering whether and how this might make sense mathematically. In many cases the characterization theorem of white noise analysis provides the user with a sweet and easy answer. Feynman's 'integral' can now be understood, the 'It's all in the vacuum' ansatz of Haag and Coester is now making sense via Dirichlet forms, and so on in many fields of application. There is mathematical finance, there have been applications in biology, and engineering, many more than we could collect in the present volume.Finally, there is one extra benefit: when we internalize the structures of Gaussian white noise analysis we will be ready to meet another close relative. We will enjoy the important similarities and differences which we encounter in the Poisson case, championed in particular by Y Kondratiev and his group. Let us look forward to a companion volume on the uses of Poisson white noise.The present volume is more than a collection of autonomous contributions. The introductory chapter on white noise analysis was made available to the other authors early on for reference and to facilitate conceptual and notational coherence in their work.
Mathematical Modelling And Numerical Methods In Finance
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Author : Alain Bensoussan
language : en
Publisher: Elsevier
Release Date : 2009-06-16
Mathematical Modelling And Numerical Methods In Finance written by Alain Bensoussan and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-06-16 with Mathematics categories.
Mathematical finance is a prolific scientific domain in which there exists a particular characteristic of developing both advanced theories and practical techniques simultaneously. Mathematical Modelling and Numerical Methods in Finance addresses the three most important aspects in the field: mathematical models, computational methods, and applications, and provides a solid overview of major new ideas and results in the three domains. - Coverage of all aspects of quantitative finance including models, computational methods and applications - Provides an overview of new ideas and results - Contributors are leaders of the field
L Vy Processes And Stochastic Calculus
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Author : David Applebaum
language : en
Publisher: Cambridge University Press
Release Date : 2009-04-30
L Vy Processes And Stochastic Calculus written by David Applebaum and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-30 with Mathematics categories.
Lévy processes form a wide and rich class of random process, and have many applications ranging from physics to finance. Stochastic calculus is the mathematics of systems interacting with random noise. Here, the author ties these two subjects together, beginning with an introduction to the general theory of Lévy processes, then leading on to develop the stochastic calculus for Lévy processes in a direct and accessible way. This fully revised edition now features a number of new topics. These include: regular variation and subexponential distributions; necessary and sufficient conditions for Lévy processes to have finite moments; characterisation of Lévy processes with finite variation; Kunita's estimates for moments of Lévy type stochastic integrals; new proofs of Ito representation and martingale representation theorems for general Lévy processes; multiple Wiener-Lévy integrals and chaos decomposition; an introduction to Malliavin calculus; an introduction to stability theory for Lévy-driven SDEs.
Malliavin Calculus In Finance
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Author : Elisa Alos
language : en
Publisher: CRC Press
Release Date : 2024-12-23
Malliavin Calculus In Finance written by Elisa Alos and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-23 with Mathematics categories.
Malliavin Calculus in Finance: Theory and Practice, Second Edition introduces the study of stochastic volatility (SV) models via Malliavin Calculus. Originally motivated by the study of the existence of smooth densities of certain random variables, Malliavin calculus has had a profound impact on stochastic analysis. In particular, it has been found to be an effective tool in quantitative finance, as in the computation of hedging strategies or the efficient estimation of the Greeks. This book aims to bridge the gap between theory and practice and demonstrate the practical value of Malliavin calculus. It offers readers the chance to discover 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. New to the Second Edition Includes a new chapter to study implied volatility within the Bachelier framework. Chapters 7 and 8 have been thoroughly updated to introduce a more detailed discussion on the relationship between implied and local volatilities, according to the new results in the literature.
The Malliavin Calculus And Related Topics
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Author : David Nualart
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-02-27
The Malliavin Calculus And Related Topics written by David Nualart and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-02-27 with Mathematics categories.
The Malliavin calculus is an infinite-dimensional differential calculus on a Gaussian space, developed to provide a probabilistic proof to Hörmander's sum of squares theorem but has found a range of applications in stochastic analysis. This book presents the features of Malliavin calculus and discusses its main applications. This second edition includes recent applications in finance and a chapter devoted to the stochastic calculus with respect to the fractional Brownian motion.
Malliavin Calculus For Levy Processes With Applications To Finance
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Author : Martin Peter Johansson
language : en
Publisher:
Release Date : 2004
Malliavin Calculus For Levy Processes With Applications To Finance written by Martin Peter Johansson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with categories.
Statistical Methods And Applications In Insurance And Finance
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Author : M'hamed Eddahbi
language : en
Publisher: Springer
Release Date : 2016-04-08
Statistical Methods And Applications In Insurance And Finance written by M'hamed Eddahbi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-08 with Mathematics categories.
This book is the outcome of the CIMPA School on Statistical Methods and Applications in Insurance and Finance, held in Marrakech and Kelaat M'gouna (Morocco) in April 2013. It presents two lectures and seven refereed papers from the school, offering the reader important insights into key topics. The first of the lectures, by Frederic Viens, addresses risk management via hedging in discrete and continuous time, while the second, by Boualem Djehiche, reviews statistical estimation methods applied to life and disability insurance. The refereed papers offer diverse perspectives and extensive discussions on subjects including optimal control, financial modeling using stochastic differential equations, pricing and hedging of financial derivatives, and sensitivity analysis. Each chapter of the volume includes a comprehensive bibliography to promote further research.
Malliavin Calculus For L Vy Processes With Applications To Finance
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Author : Giulia Di Nunno
language : en
Publisher:
Release Date : 2009
Malliavin Calculus For L Vy Processes With Applications To Finance written by Giulia Di Nunno and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Lévy processes categories.
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.
Malliavin Calculus And Its Applications
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Author : David Nualart
language : en
Publisher: American Mathematical Soc.
Release Date : 2009
Malliavin Calculus And Its Applications written by David Nualart and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
The 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.