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| Author | : Giulia Di Nunno |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 421 |
| Release | : 2008-10-08 |
| Genre | : Mathematics |
| ISBN | : 3540785728 |
Download Malliavin Calculus for Lévy Processes with Applications to Finance Book in PDF, ePub and Kindle
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 | : |
| Total Pages | : 413 |
| Release | : 2009 |
| Genre | : Lévy processes |
| ISBN | : 9781282631724 |
Download Malliavin Calculus for Lévy Processes with Applications to Finance Book in PDF, ePub and Kindle
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 |
| Total Pages | : 461 |
| Release | : 2009-04-30 |
| Genre | : Mathematics |
| ISBN | : 1139477986 |
Download Lévy Processes and Stochastic Calculus Book in PDF, ePub and Kindle
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 | : Jiro Akahori |
| Publisher | : World Scientific |
| Total Pages | : 228 |
| Release | : 2006 |
| Genre | : Mathematics |
| ISBN | : 9812565191 |
Download Stochastic Processes and Applications to Mathematical Finance Book in PDF, ePub and Kindle
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 | : David Nualart |
| Publisher | : Cambridge University Press |
| Total Pages | : 249 |
| Release | : 2018-09-27 |
| Genre | : Business & Economics |
| ISBN | : 1107039126 |
Download Introduction to Malliavin Calculus Book in PDF, ePub and Kindle
A compact introduction to this active and powerful area of research, combining basic theory, core techniques, and recent applications.
| Author | : M'hamed Eddahbi |
| Publisher | : Springer |
| Total Pages | : 225 |
| Release | : 2016-04-08 |
| Genre | : Mathematics |
| ISBN | : 3319304178 |
Download Statistical Methods and Applications in Insurance and Finance Book in PDF, ePub and Kindle
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 |
| Total Pages | : 429 |
| Release | : 2012-03 |
| Genre | : Mathematics |
| ISBN | : 1107016142 |
Download Malliavin Calculus for Lévy Processes and Infinite-Dimensional Brownian Motion Book in PDF, ePub and Kindle
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 |
| Total Pages | : 580 |
| Release | : 2013-02-15 |
| Genre | : Mathematics |
| ISBN | : 1461459060 |
Download Malliavin Calculus and Stochastic Analysis Book in PDF, ePub and Kindle
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 | : Jiro Akahori |
| Publisher | : World Scientific |
| Total Pages | : 410 |
| Release | : 2004 |
| Genre | : Mathematics |
| ISBN | : 9812387781 |
Download Stochastic Processes and Applications to Mathematical Finance Book in PDF, ePub and Kindle
This book contains articles on stochastic processes (stochastic calculus and Malliavin calculus, functionals of Brownian motions and Levy processes, stochastic control and optimization problems, stochastic numerics, and so on) and their applications to problems in mathematical finance. Examples of topics are applications of Malliavin calculus and numerical analysis to a new simulation scheme for calculating the price of financial derivatives, applications of the asymptotic expansion method in Malliavin calculus to financial problems, semimartingale decompositions under an enlargement of filtrations in connection with insider problems, and the problem of transaction costs in connection with stochastic control and optimization problems.
| Author | : Andrea Pascucci |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 727 |
| Release | : 2011-04-15 |
| Genre | : Mathematics |
| ISBN | : 8847017815 |
Download PDE and Martingale Methods in Option Pricing Book in PDF, ePub and Kindle
This book offers an introduction to the mathematical, probabilistic and numerical methods used in the modern theory of option pricing. The text is designed for readers with a basic mathematical background. The first part contains a presentation of the arbitrage theory in discrete time. In the second part, the theories of stochastic calculus and parabolic PDEs are developed in detail and the classical arbitrage theory is analyzed in a Markovian setting by means of of PDEs techniques. After the martingale representation theorems and the Girsanov theory have been presented, arbitrage pricing is revisited in the martingale theory optics. General tools from PDE and martingale theories are also used in the analysis of volatility modeling. The book also contains an Introduction to Lévy processes and Malliavin calculus. The last part is devoted to the description of the numerical methods used in option pricing: Monte Carlo, binomial trees, finite differences and Fourier transform.
