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| Author | : Giulia Di Nunno |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 421 |
| Release | : 2008-10-08 |
| Genre | : Mathematics |
| ISBN | : 3540785728 |
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 | : David Applebaum |
| Publisher | : Cambridge University Press |
| Total Pages | : 461 |
| Release | : 2009-04-30 |
| Genre | : Mathematics |
| ISBN | : 1139477986 |
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 | : Giulia Di Nunno |
| Publisher | : |
| Total Pages | : 413 |
| Release | : 2009 |
| Genre | : Lévy processes |
| ISBN | : 9781282631724 |
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 | : Cambridge University Press |
| Total Pages | : 249 |
| Release | : 2018-09-27 |
| Genre | : Business & Economics |
| ISBN | : 1107039126 |
A compact introduction to this active and powerful area of research, combining basic theory, core techniques, and recent applications.
| Author | : Frederi Viens |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 580 |
| Release | : 2013-02-15 |
| Genre | : Mathematics |
| ISBN | : 1461459060 |
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 | : Hiroyuki Matsumoto |
| Publisher | : Cambridge University Press |
| Total Pages | : 359 |
| Release | : 2017 |
| Genre | : Mathematics |
| ISBN | : 110714051X |
Developing the Itô calculus and Malliavin calculus in tandem, this book crystallizes modern day stochastic analysis into a single volume.
| Author | : Horst Osswald |
| Publisher | : Cambridge University Press |
| Total Pages | : 429 |
| Release | : 2012-03 |
| Genre | : Mathematics |
| ISBN | : 1107016142 |
After functional, measure and stochastic analysis prerequisites, the author covers chaos decomposition, Skorohod integral processes, Malliavin derivative and Girsanov transformations.
| Author | : Andrea Pascucci |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 727 |
| Release | : 2011-04-15 |
| Genre | : Mathematics |
| ISBN | : 8847017815 |
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.
| Author | : Stefano M. Iacus |
| Publisher | : John Wiley & Sons |
| Total Pages | : 402 |
| Release | : 2011-02-23 |
| Genre | : Business & Economics |
| ISBN | : 1119990203 |
Presents inference and simulation of stochastic process in the field of model calibration for financial times series modelled by continuous time processes and numerical option pricing. Introduces the bases of probability theory and goes on to explain how to model financial times series with continuous models, how to calibrate them from discrete data and further covers option pricing with one or more underlying assets based on these models. Analysis and implementation of models goes beyond the standard Black and Scholes framework and includes Markov switching models, Lévy models and other models with jumps (e.g. the telegraph process); Topics other than option pricing include: volatility and covariation estimation, change point analysis, asymptotic expansion and classification of financial time series from a statistical viewpoint. The book features problems with solutions and examples. All the examples and R code are available as an additional R package, therefore all the examples can be reproduced.
| Author | : Paul Malliavin |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 148 |
| Release | : 2006-02-25 |
| Genre | : Business & Economics |
| ISBN | : 3540307990 |
Highly esteemed author Topics covered are relevant and timely
