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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
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.
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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.
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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Computation of the Delta in Multidimensional Jump-Diffusion Setting with Applications to Stochastic Volatility Models
TL;DR: In this paper, the robustness of options prices to model variation in a multidimensional jump-diffusion framework was studied for both European and Exotic options and their deltas using two approaches: the Malliavin method and the Fourier method.
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Hedging of defaultable claims in a structural model using a locally risk-minimizing approach
TL;DR: In this article, the problem of hedging defaultable claims and their Follmer-Schweizer decompositions is discussed in a structural model, where the underlying process is a finite variation Levy process and the claims pay a predetermined payout at maturity, contingent on no prior default.
Posted Content
Optimal Stopping for Strong Markov Processes : Explicit solutions and verification theorems for diffusions, multidimensional diffusions, and jump-processes.
TL;DR: In this article, the authors consider the optimal stopping problem of a strong Markov process, with a reward function and a discount rate, and find the stopping time such that the expected reward at the time of stopping is maximized.
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Regularity of the density of a stable-like driven SDE with Hölder continuous coefficients
Arturo Kohatsu-Higa,Libo Li +1 more
TL;DR: In this paper, the authors used the backward parametrix method to prove the existence and regularity of the transition density associated to the solution process of a stable-like driven stochastic differential equation with Holder continuous coefficients.
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Reduced α-stable dynamics for multiple time scale systems forced with correlated additive and multiplicative Gaussian white noise.
TL;DR: This study considers the stochastic averaging of systems where a linear CAM noise process in the infinite variance parameter regime drives a comparatively slow process and identifies the conditions required for the fast linear CAM process to have such an influence in driving a slower process and derives an (effectively) equivalent fast, infinite-variance process for which an existing stochastically averaging approximation is readily applied.