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Lévy processes and infinitely divisible distributions
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
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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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Construction and heat kernel estimates of general stable-like Markov processes
TL;DR: In this paper, a strong Feller process with a transition density is defined as a sum of an explicitly given principal term and a residual term, which is the transition density of an α-stable random variable whose parameters depend on the current state of the process.
Journal ArticleDOI
Pricing and Hedging of Lookback Options in Hyper-exponential Jump Diffusion Models
Markus Hofer,Philipp Mayer +1 more
TL;DR: In this article, the problem of pricing lookback options in certain exponential Levy market models is considered, where the lookback option price can be expressed as one-dimensional Laplace transform.
Journal ArticleDOI
A note on convergence of option prices and their Greeks for Lévy models
TL;DR: In this paper, the authors consider geometric Levy models in which the infinite activity of the small jumps is approximated by a scaled Brownian motion and study the robustness of option prices to model variation after a change of measure where the measure depends on the model choice.
Journal ArticleDOI
On fluctuation theory for spectrally negative Lévy processes with Parisian reflection below, and applications
Florin Avram,Xiaowen Zhou +1 more
TL;DR: In this article, a collection of first passage formulas for spectrally negative Parisian Levy processes, expressed in terms of $W,Z$ is presented, which may serve as an "instruction kit" for computing quantities of interest in applications, for example in risk theory and mathematical finance.
Dissertation
Price feedback and hybrid diffusions in finance
TL;DR: This investigation seeks to motivate a new class of models, throwing out the stationary increments hypothesis, and argues that certain techniques of trading decision-making are not independent of previous price movements, and the returns will reflect that.