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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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On the predictable representation property of martingales associated with Lévy processes
TL;DR: In this paper, the predictable representation property (PRP) in the frame of Levy processes is investigated and the main result is that any total system in leads to a family of martingales with the PRP.
Journal ArticleDOI
Modelling and Prediction of Financial Time Series
TL;DR: In this paper, the authors consider statistical aspects of the modeling and prediction theory of time series in one and many dimensions, and discuss Levy-based and general models, and the stationary and non-stationary cases.
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On the Capital Allocation Problem for a New Coherent Risk Measure in Collective Risk Theory
TL;DR: In this article, a new coherent cumulative risk measure on a subclass in the space of cadlag processes is introduced. And the problem of capital allocation for this risk measure has a unique solution determined by the Euler allocation method.
Software for "Near-optimal estimation of jump activity in semimartingales"
TL;DR: An R script generating the data in the paper "Near-optimal estimation of jump activity in semimartingales" is described in this article, where the authors present an R script that generates the data.
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Packing dimension results for anisotropic Gaussian random fields
TL;DR: In this paper, the authors extend the original notion of packing dimension profile due to Falconer and Howroyd (1997) to the anisotropic metric space, and study the packing dimension of the range $X(E), where $E is a Borel set.
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.