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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
Citations
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Journal ArticleDOI
Dirichlet curves, convex order and Cauchy distribution
Gérard Letac,Mauro Piccioni +1 more
TL;DR: The present paper shows that if $m$ exists and if $\psi$ is a convex function on $\mathbb{R}^{d}$ then $t\mapsto\int_{\mathbb(R)^{d})d}}\psi(x)mu(t\alpha)(dx) $ is a decreasing function, which means that t\mapSto\mu( t\alpha)$ is decreasing according to the Strassen convex
Journal ArticleDOI
Comparison of Markov processes via infinitesimal generators
Ludger Rüschendorf,Viktor Wolf +1 more
TL;DR: In this article, the authors derived comparison results for Markov processes with respect to stochastic orderings induced by function classes, and showed that the monotonicity of one process and comparability of the infinitesimal generators implies ordering of the processes.
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Convex Order of Discrete, Continuous, and Predictable Quadratic Variation and Applications to Options on Variance
TL;DR: For a class of models including independently time-changed Levy models and Sato processes with symmetric jumps, the results show that options on variance are typically underpriced if quadratic variation is substituted for the discretely sampled realized variance.
Journal ArticleDOI
Nonparametric Bayesian analysis of the compound Poisson prior for support boundary recovery
TL;DR: In this paper, the authors derived a limiting shape result for a compound Poisson process prior and a function space with increasing parameter dimension, and showed that the marginal posterior of the mean functional performs an automatic bias correction and contracts with a faster rate than the MLE.
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Finite Difference Methods for Option Pricing under Lévy Processes: Wiener-Hopf Factorization Approach
TL;DR: The goal of the paper is to incorporate the Wiener-Hopf factorization into finite difference methods for pricing options in Lévy models with jumps, applicable for pricing barrier and American options.
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.