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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
LAN property for an ergodic diffusion with jumps
TL;DR: In this article, a multidimensional ergodic diffusion with jumps driven by a Brownian motion and a Poisson random measure associated with a compound Poisson process, whose drift coefficient depends on an unknown parameter, is considered.
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Strong law of large numbers for supercritical superprocesses under second moment condition
TL;DR: In this article, the authors consider a supercritical superprocess X = {X====== t====== t>>\s, t ≥ 0} on a locally compact separable metric space (E,m) and show that the exceptional set in the above limit does not depend on the initial measure µ and the function f.
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Behavior of long-term yields in a lévy term structure
TL;DR: In this paper, the long-term yield in a HJM setting for forward rates driven by Levy processes is investigated by examining continuously compounded spot rate yields with maturity going to infinity, and the main results are that the longterm volatility has to vanish except in the case of a Levy process with only negative jumps and paths of finite variation serving as random driver.
Journal ArticleDOI
Pricing American options under jump-diffusion models using local weak form meshless techniques
Jamal Amani Rad,Kourosh Parand +1 more
TL;DR: This paper proposes the local weak form meshless methods for option pricing under Merton and Kou jump-diffusion models and focuses on meshless local Petrov–Galerkin, local boundary integral equation methods based on moving least square approximation and local radial point interpolation based on Wendland's compactly supported radial basis functions.
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Nonparametric implied Lévy densities
Likuan Qin,Viktor Todorov +1 more
TL;DR: In this paper, a nonparametric estimator for the Levy density of an asset price, following an Ito semimartingale, implied by short-maturity options, is developed.
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.