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Lévy processes and infinitely divisible distributions
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
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Journal ArticleDOI
A Characterization of the Gaussian Distribution
TL;DR: In this paper, a partial reverse of this theorem is proved: if X 1, X, X n are independent infinitely divisible random variables such that has the chi-square distribution with n degrees of freedom then random variables X 1.
Journal ArticleDOI
Markov chain approximations to scale functions of Lévy processes
TL;DR: In this article, a general algorithm for the computation of the scale functions of a spectrally negative Levy process X, based on a natural weak approximation of X via upwards skip-free continuous-time Markov chains with stationary independent increments, is presented.
Posted Content
The Density of Distributions from the Bondesson Class
TL;DR: In this paper, an integral representation for the density of distributions from the Bondesson class, a large subclass of positive, infinitely divisible distributions, is derived, which significantly enlarges the class of numerically tractable stochastic time transformations.
Journal ArticleDOI
A variation of the Canadisation algorithm for the pricing of American options driven by Lévy processes
Florian Kleinert,Kees van Schaik +1 more
TL;DR: In this article, the authors introduce an algorithm for the pricing of finite expiry American options driven by Levy processes and show that the adjusted algorithm is viable for any Levy process whose law at an independent, exponentially distributed time consists of a (possibly infinite) mixture of exponentials.
Posted Content
Transform-Based Evaluation of Prices and Greeks of Lookback Options Driven by Lévy Processes
Naser M. Asghari,Michel Mandjes +1 more
TL;DR: In this paper, the authors developed a technique based on numerical inversion to compute the prices and Greeks of lookback options driven by Levy processes, where the Wiener-Hopf decomposition provides all the probabilistic information needed to evaluate these prices.
References
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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.