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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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Construction of continuous-state branching processes in varying environments
Rongjuan Fang,Zenghu Li +1 more
TL;DR: In this article, a continuous-state branching process in varying environments is constructed by the pathwise unique solution to a stochastic integral equation driven by time-space noises, and the behavior of the continuous state process at its bottlenecks is clarified.
Journal Article
On the class of distributions of subordinated Lévy processes
Orimar Sauri,Almut E. D. Veraart +1 more
TL;DR: In this paper, the authors studied the class of distributions obtained by subordinating Levy processes and Levy bases and derived properties of a suitable mapping obtained via Levy mixing, which can be used to solve the recovery problem for general Levy bases as well as for moving average processes which are driven by subordinated Levy processes.
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Quadratic BSDEs with jumps and related non-linear expectations: a fixed-point approach ∗
TL;DR: In this paper, the existence of bounded solutions of quadratic backward SDEs with jumps was proved using a direct fixed point approach as in Tevzadze [36].
Journal ArticleDOI
Lévy processes with finite variance conditioned to avoid an interval
TL;DR: In this paper, the authors studied the question if a Levy process can be conditioned to avoid an interval and, if so, the path behavior of the conditioned process, and they showed that conditioning is possible for Levy processes with finite second moments.
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Pricing and Hedging in Affine Models with Possibility of Default
TL;DR: A Heston-type Stochastic volatility model with possibility of default and stochastic interest rates is discussed, and an efficient method to compute prices of power payoffs is shown by solving a coupled system of generalized Riccati equations.
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.