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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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Pricing approximations and error estimates for local L\'evy-type models with default
TL;DR: In this paper, approximate solutions of partial integro-differential equations, which arise in financial models when defaultable assets are described by general scalar Levy-type stochastic processes, are derived.
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Boundary regularity for nonlocal operators with kernels of variable orders.
TL;DR: In this article, the boundary regularity of Dirichlet solutions with a kernel of variable orders was studied in the generalized H\"older space, where the order of differentiability of the kernel is not represented by a single number.
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Asymptotic Distributions of the Overshoot and Undershoots for the L\'evy Insurance Risk Process in the Cram\'er and Convolution Equivalent Cases
TL;DR: In this article, the authors derived the asymptotics of the distributions of the overshoot and undershoots of a high level, for a Levy process which drifts to $-\infty$ and satisfies a Cramer or a convolution equivalent condition.
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Robust consumption-investment problem under CRRA and CARA utilities with time-varying confidence sets
Zongxia Liang,Ming Ma +1 more
TL;DR: In this paper, a robust consumption-investment problem under constant relative risk aversion and constant absolute risk aversion utilities is considered, and the time-varying confidence sets are specified by Θ, a correspondence from [0, T] to the space of the Levy triplets, and describe a priori drift, volatility, and jump information.
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Stable processes conditioned to avoid an interval
TL;DR: In this paper, it was shown that conditioning stable Markov processes to avoid an interval is possible in the classical sense and that the resulting process is a Doob h -transform of the stable process killed on entering the aforesaid interval.
References
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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.
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.