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
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
More filters
Journal ArticleDOI
A multiplicative short proof for the unimodality of stable densities
TL;DR: In this paper, Chernin and Ibragimov showed that their approach to deduce the general case from the extremal ones, whose completion contained an error as discovered later by Kanter, can be carried out successfully in considering Bochner's subordination and multiplicative strong unimodality.
Journal ArticleDOI
Some recent advances for limit theorems
TL;DR: In this article, the authors present some recent developments for limit theorems in probability theory, illustrating the variety of this field of activity, from Stein's method, to asymptotics for some discrete models.
Posted Content
Option Pricing with Greed and Fear Factor: The Rational Finance Approach
TL;DR: In this article, the main concepts of Prospect Theory and Cumulative Prospect Theory within the framework of rational dynamic asset pricing theory are explained and option pricing formulas when asset returns are altered with a generalized Prospect Theory value function or a modified Prelec weighting probability function.
Posted Content
Optimal dividends problem with a terminal value for spectrally positive Levy processes
Chuancun Yin,Yuzhen Wen +1 more
TL;DR: In this article, the authors considered a modified version of the classical optimal dividends problem of de Finetti in which the dividend payments subject to a penalty at ruin were modeled by a general spectrally positive Levy process before dividends are deducted.
Journal ArticleDOI
Weak Drifts of Infinitely Divisible Distributions and Their Applications
Ken-iti Sato,Yohei Ueda +1 more
TL;DR: Weak drift of an infinitely divisible distribution μ on ℝd is defined by analogy with weak mean; properties and applications of weak drift are given in this article, where the weak drift of μ equals the minus of the weak mean of the inversion μ′ of μ.