Stochastic Integration with Jumps - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Stochastic Integration with Jumps write by Klaus Bichteler. This book was released on 2002-05-13. Stochastic Integration with Jumps available in PDF, EPUB and Kindle. The complete theory of stochastic differential equations driven by jumps, their stability, and numerical approximation theories.
PDE and Martingale Methods in Option Pricing
PDE and Martingale Methods in Option Pricing - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook PDE and Martingale Methods in Option Pricing write by Andrea Pascucci. This book was released on 2011-04-15. PDE and Martingale Methods in Option Pricing available 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.
Applied Stochastic Control of Jump Diffusions
Applied Stochastic Control of Jump Diffusions - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Applied Stochastic Control of Jump Diffusions write by Bernt Øksendal. This book was released on 2007-04-26. Applied Stochastic Control of Jump Diffusions available in PDF, EPUB and Kindle. Here is a rigorous introduction to the most important and useful solution methods of various types of stochastic control problems for jump diffusions and its applications. Discussion includes the dynamic programming method and the maximum principle method, and their relationship. The text emphasises real-world applications, primarily in finance. Results are illustrated by examples, with end-of-chapter exercises including complete solutions. The 2nd edition adds a chapter on optimal control of stochastic partial differential equations driven by Lévy processes, and a new section on optimal stopping with delayed information. Basic knowledge of stochastic analysis, measure theory and partial differential equations is assumed.
Lévy Processes and Stochastic Calculus
Lévy Processes and Stochastic Calculus - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lévy Processes and Stochastic Calculus write by David Applebaum. This book was released on 2009-04-30. Lévy Processes and Stochastic Calculus available 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.
Introduction to Stochastic Calculus with Applications
Introduction to Stochastic Calculus with Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Introduction to Stochastic Calculus with Applications write by Fima C. Klebaner. This book was released on 2005. Introduction to Stochastic Calculus with Applications available in PDF, EPUB and Kindle. This book presents a concise treatment of stochastic calculus and its applications. It gives a simple but rigorous treatment of the subject including a range of advanced topics, it is useful for practitioners who use advanced theoretical results. It covers advanced applications, such as models in mathematical finance, biology and engineering.Self-contained and unified in presentation, the book contains many solved examples and exercises. It may be used as a textbook by advanced undergraduates and graduate students in stochastic calculus and financial mathematics. It is also suitable for practitioners who wish to gain an understanding or working knowledge of the subject. For mathematicians, this book could be a first text on stochastic calculus; it is good companion to more advanced texts by a way of examples and exercises. For people from other fields, it provides a way to gain a working knowledge of stochastic calculus. It shows all readers the applications of stochastic calculus methods and takes readers to the technical level required in research and sophisticated modelling.This second edition contains a new chapter on bonds, interest rates and their options. New materials include more worked out examples in all chapters, best estimators, more results on change of time, change of measure, random measures, new results on exotic options, FX options, stochastic and implied volatility, models of the age-dependent branching process and the stochastic Lotka-Volterra model in biology, non-linear filtering in engineering and five new figures.Instructors can obtain slides of the text from the author.
