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Lévy processes and infinitely divisible distributions
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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
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Fluctuations of Lévy Processes with Applications
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Ten equivalent definitions of the fractional laplace operator
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Optimal stopping and perpetual options for Lévy processes
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Density and tails of unimodal convolution semigroups
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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.
References
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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.
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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.
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On Dynamic Spectral Risk Measures and a Limit Theorem
TL;DR: In this paper, a class of dynamic spectral risk measures is introduced in terms of a certain family of g-expectations driven by Wiener and Poisson point processes, which are locally law-invariant and additive on the set of pathwise increasing random variables.