Open AccessBook
Lévy processes and infinitely divisible distributions
Reads0
Chats0
TLDR
In this paper, the authors consider the distributional properties of Levy processes and propose a potential theory for Levy processes, which is based on the Wiener-Hopf factorization.Abstract:
Preface to the revised edition Remarks on notation 1. Basic examples 2. Characterization and existence 3. Stable processes and their extensions 4. The Levy-Ito decomposition of sample functions 5. Distributional properties of Levy processes 6. Subordination and density transformation 7. Recurrence and transience 8. Potential theory for Levy processes 9. Wiener-Hopf factorizations 10. More distributional properties Supplement Solutions to exercises References and author index Subject index.read more
Citations
More filters
Journal ArticleDOI
Estimation for L\'{e}vy processes from high frequency data within a long time interval
TL;DR: In this paper, a nonparametric estimation of the Levy density for Levy processes, with and without Brownian component, is presented, and a bound for the global L 2 risk is provided.
Journal ArticleDOI
Exponential moments of affine processes
TL;DR: In this article, the maximal domain of the moment generating function of affine processes was investigated and the validity of the affine transform formula that connects exponential moments with the solution of a generalized Riccati differential equation was shown.
Journal ArticleDOI
SDEs driven by a time-changed Lévy process and their associated time-fractional order pseudo-differential equations
TL;DR: In this article, the transition probabilities of a solution to a classical Ito stochastic differential equation (SDE) satisfy in the weak sense the associated Kolmogorov equation, a partial differential equation with coefficients determined by the corresponding SDE.
Journal ArticleDOI
Tempered Infinitely Divisible Distributions and Processes
TL;DR: In this article, a modification of the tempering function allows one to obtain suitable properties of the Rosinski setting, in particular, TID distributions may have exponential moments of any order and conserve all proper properties.
Journal ArticleDOI
Efficient Option Pricing by Frame Duality with the Fast Fourier Transform
TL;DR: A method for efficiently inverting analytic characteristic functions using frame projection, as in the case of Heston's model and exponential Levy models, is developed and convergence is demonstrated for geometric Asian options as well as the pricing of baskets of European options.
References
More filters
BookDOI
Fluctuations of Lévy Processes with Applications
TL;DR: In this article, Kloeden, P., Ombach, J., Cyganowski, S., Kostrikin, A. J., Reddy, J.A., Pokrovskii, A., Shafarevich, I.A.
Journal ArticleDOI
Ten equivalent definitions of the fractional laplace operator
TL;DR: In this article, several definitions of the Riesz fractional Laplace operator in R^d have been studied, including singular integrals, semigroups of operators, Bochner's subordination, and harmonic extensions.
Book ChapterDOI
The Theory of Scale Functions for Spectrally Negative Lévy Processes
TL;DR: In this article, the authors give an up-to-date account of the theory and applications of scale functions for spectrally negative Levy processes, including the first extensive overview of how to work numerically with scale functions.
Journal ArticleDOI
Optimal stopping and perpetual options for Lévy processes
TL;DR: A closed formula for prices of perpetual American call options in terms of the overall supremum of the Lévy process, and a corresponding closed formulas for perpetual American put options involving the infimum of the after-mentioned process are obtained.
Extreme Events: Dynamics, Statistics and Prediction
TL;DR: In this paper, the authors review work on extreme events, their causes and consequences, by a group of European and American researchers involved in a three-year project on these topics.