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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
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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.
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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.
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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.
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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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Numerical inverse Lévy measure method for infinite shot noise series representation
Junichi Imai,Reiichiro Kawai +1 more
TL;DR: The proposed numerical approach to the inverse Levy measure method enables one to simulate entire approximate trajectory of stochastic differential equations with jumps based on infinite shot noise series representation and has the potential to yield substantial improvements in simulation time and estimator efficiency.
Posted Content
Variance Swaps on Defaultable Assets and Market Implied Time-Changes
TL;DR: This work provides an explicit formula for the value of a variance swap when the underlying is modeled as a Markov process time changed by a L\'{e}vy subordinator, allowing for joint valuation of credit and equity derivatives as well as variance swaps.
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Further examples of GGC and HCM densities
Wissem Jedidi,Thomas Simon +1 more
TL;DR: In this paper, the authors gave stronger credit to Bondesson's hypothesis that positive α-stable densities are hyperbolically completely monotone whenever α ≤ 1 1/2.
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Polynomial Jump-Diffusion Models
Damir Filipović,Martin Larsson +1 more
TL;DR: A large class of novel financial asset pricing models that are based on polynomial jump-diffusions are introduced, including a generic method for option pricing based on moment expansions.
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Local Time Asymptotics for Centered Lévy Processes with Two-Sided Reflection
TL;DR: In this article, the authors studied the local times of a Levy process reflected at two barriers 0 and K > 0 and derived asymptotics for l K when the Levy process has mean zero.