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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
Pricing Barrier and Bermudan Style Options Under Time-Changed Levy Processes: Fast Hilbert Transform Approach
Pingping Zeng,Yue Kuen Kwok +1 more
TL;DR: In this paper, the authors proposed a fast Hilbert transform approach for pricing discretely monitored barrier and Bermudan style options under time-changed Levy processes by applying the Fast Hilbert Transform (FHT) method to the log-asset return dimension and quadrature rule to the dimension of log-activity rate of stochastic time change.
Posted Content
Exit problems for positive self-similar Markov processes with one-sided jumps
Matija Vidmar,Matija Vidmar +1 more
TL;DR: In this article, a systematic exposition of scale functions for positive self-similar Markov processes with one-sided jumps is given, expressing as convolution series of the usual scale functions associated with spectrally onesided Levy processes that underly the pssMp through the Lamperti transform.
Posted Content
Stationary and multi-self-similar random fields with stochastic volatility
TL;DR: In this paper, the authors introduce stationary and multi-self-similar random fields which account for stochastic volatility and have type G marginal law, and two methods for parameterising the weight functions in the moving average representation are presented.
Journal ArticleDOI
Strong renewal theorems with infinite mean beyond local large deviations
TL;DR: The strong renewal theorem for a random walk with step distribution was established in this paper, by extending the large deviations approach in Doney [Probab. Theory Related Fileds 107 (1997) 451-465].
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.