Open AccessBook
Lévy processes and infinitely divisible distributions
Reads0
Chats0
TLDR
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
More filters
Posted Content
Bounded size bias coupling: a Gamma function bound, and universal Dickman-function behavior
TL;DR: For the class of infinitely divisible distributions with finite mean, whose Levy measure is supported on an interval contained in $[0,c]$ for some $c < \infty, the upper tail probability is shown to decay at least as fast as the reciprocal of a Gamma function, guaranteeing a moment generating function that converges everywhere as mentioned in this paper.
Journal ArticleDOI
Pricing and hedging Asian-style options on energy
Fred Espen Benth,Nils Detering +1 more
TL;DR: In this paper, the problem of pricing and hedging Asian-style options on energy with a quadratic risk criterion when trading in the underlying future is restricted is solved by using moment matching techniques.
Journal ArticleDOI
The smooth-fit property in an exponential Lévy model
TL;DR: In this paper, the smooth-fit property of the American put price with finite maturity in an exponential Levy model was studied, where the underlying stock pays dividends at a continuous rate.
Posted Content
An anticipating Ito formula for Levy processes
TL;DR: In this article, an anticipative version of the change-of-variable formula for Levy processes is obtained in the domain of the anihilation (gradient) operator in the "future sense".
Proceedings Article
Nonconvex Penalization Using Laplace Exponents and Concave Conjugates
Zhihua Zhang,Bojun Tu +1 more
TL;DR: It is shown that the nonconvex logarithmic and exponential penalty functions are the Laplace exponents of Gamma and compound Poisson subordinators, respectively, and the relationship between these two penalties is due to asymmetricity of the KL distance.
References
More filters
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.