Open AccessBook
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
Efficient pricing of swing options in Lévy-driven models
TL;DR: In this article, the problem of pricing swing options with multiple exercise rights in Levy-driven models was considered and an efficient Wiener-Hopf factorization method was proposed to solve multiple parabolic partial integro-differential equations associated with the pricing problem.
Journal ArticleDOI
Prediction in a mixed Poisson cluster model
Muneya Matsui,Tomasz Rolski +1 more
TL;DR: In this paper, a mixed Poisson cluster model is considered, where the cluster center process is a mixed poisson process and descendant processes are additive processes, and the authors derive computationally reasonable expressions for predictors and their variances.
Dissertation
Stochastic analysis with Lévy noise in the dual of a nuclear space
Fonseca Mora,Christian Andrés +1 more
TL;DR: In this article, a new theory of stochastic analysis with respect to Levy processes in the strong dual of a nuclear space is introduced, and conditions for the existence of continuous and cadlag versions taking values in a Hilbert space continuously included on the dual space are also provided.
Journal ArticleDOI
Option Implied VIX, Skew and Kurtosis Term Structures
Dilip B. Madan,King Wang +1 more
TL;DR: In this article, the CBOE skew index was compared with those derived from parametric skews of bilateral gamma models and from the differentiation of option implied characteristic exponents, and the remedy suggested employs a finer and wider set of strikes obtaining additional option prices by interpolation and extrapolation of implied volatilities.
Posted Content
Marchenko-Pastur Theorem and Bercovici-Pata bijections for heavy-tailed or localized vectors
TL;DR: In this article, the authors generalize the Marchenko-pastur theorem to a quite general framework, including random projections whose corresponding vectors are localized, i.e. with some components much larger than the other ones.
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.