Malliavin Calculus for Lévy Processes with Applications to Finance PDF Download

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 Applebaum
Publisher: Cambridge University Press
ISBN: 1139477986
Category : Mathematics
Languages : en
Pages : 461

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Book Description
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.

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: Jiro Akahori
Publisher: World Scientific
ISBN: 9812565191
Category : Mathematics
Languages : en
Pages : 228

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Book Description
Based around recent lectures given at the prestigious Ritsumeikan conference, the tutorial and expository articles contained in this volume are an essential guide for practitioners and graduates alike who use stochastic calculus in finance.Among the eminent contributors are Paul Malliavin and Shinzo Watanabe, pioneers of Malliavin Calculus. The coverage also includes a valuable review of current research on credit risks in a mathematically sophisticated way contrasting with existing economics-oriented articles.

Author: M'hamed Eddahbi
Publisher: Springer
ISBN: 3319304178
Category : Mathematics
Languages : en
Pages : 225

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Book Description
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.

Author: Horst Osswald
Publisher: Cambridge University Press
ISBN: 1107016142
Category : Mathematics
Languages : en
Pages : 429

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Book Description
After functional, measure and stochastic analysis prerequisites, the author covers chaos decomposition, Skorohod integral processes, Malliavin derivative and Girsanov transformations.

Author: Frederi Viens
Publisher: Springer Science & Business Media
ISBN: 1461459060
Category : Mathematics
Languages : en
Pages : 580

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Book Description
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.

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

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Book Description

Author: David Nualart
Publisher: Springer Science & Business Media
ISBN: 1475724373
Category : Mathematics
Languages : en
Pages : 273

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Book Description
The 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.