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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
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.
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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.
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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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Proceedings ArticleDOI
Modeling and linearization of systems under heavy-tailed stochastic noise with application to renewable energy assessment
TL;DR: This work investigates models based on stable processes, and proposes a method for stochastic linearization that is applied to renewable energy assessment to show the effectiveness.
Journal ArticleDOI
Electricity futures price modeling with lévy term structure models
TL;DR: In this paper, the authors generalize the approach of Hinz & Wilhelm (2006), pricing flow commodity derivatives using fixed income market techniques, replacing in the dynamics of the asset prices the Brownian motion by a more general Levy process, also taking into account the occurrence of spikes.
Book ChapterDOI
Derivative Pricing under the Possibility of Long Memory in the supOU Stochastic Volatility Model
Robert Stelzer,Jovana Zavišin +1 more
TL;DR: In this paper, the authors consider the supOU stochastic volatility model and give conditions for the discounted stock price to be a martingale, calculate the characteristic function, give a strip where it is analytic, and discuss the use of Fourier pricing techniques.
Journal ArticleDOI
Solvability of the nonlinear dirichlet problem with integro-differential operators
Erhan Bayraktar,Qingshuo Song +1 more
TL;DR: The construction of the supersolution required in Perron's method is achieved by solving the exit time problem of an Ito jump diffusion and relying on the proof of continuity of the entrance time and point with respect to the Skorokhod topology.