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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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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.
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.
Journal ArticleDOI
Density and tails of unimodal convolution semigroups
TL;DR: For the isotropic unimodal probability convolutional semigroups, this article gave sharp bounds for their Levy-Khintchine exponent with Matuszewska indices strictly between 0 and 2.
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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Journal ArticleDOI
Variance-Optimal Hedging for Time-Changed Lévy Processes
Jan Kallsen,Arnd Pauwels +1 more
TL;DR: In this paper, the variance-optimal hedging problem in stochastic volatility (SV) models based on time-changed Levy processes was solved in the setup of Carr et al. (2003).
Journal ArticleDOI
Options pricing under the one-dimensional jump-diffusion model using the radial basis function interpolation scheme
Ron Chan,Simon Hubbert +1 more
TL;DR: In this article, a cubic spline radial basis function (RBF) interpolation scheme was used to compute European and American option prices under the jump-diffusion model using the RBF interpolation algorithm.
Book ChapterDOI
Path Properties and Regularity of Affine Processes on General State Spaces
Christa Cuchiero,Josef Teichmann +1 more
TL;DR: In this paper, a new proof for the regularity of affine processes on general state spaces was provided by methods from the theory of Markovian semimartingales, and it was shown that the definition of an affine process, namely as stochastically continuous time-homogeneous Markov process with exponential affine Fourier-Laplace transform, already implies the existence of a cadlag version.
Posted Content
A wiener-hopf type factorization for the exponential functional of l ´
TL;DR: In this paper, the authors define the exponential functional of a Levy process as follows I� = Z ∞ 0 e e � t dt for mild conditions on � and show that the following factorization of exponential functionals I� d = IH × IY holds.
Journal ArticleDOI
Second Order BSDEs with Jumps: Formulation and Uniqueness
TL;DR: In this paper, the authors define a notion of second-order backward stochastic differential equations with jumps (2BSDEJs for short), which generalizes the continuous case considered by Soner, Touzi and Zhang.