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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.
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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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Contingent Capital: Valuation and Risk Implications Under Alternative Conversion Mechanisms
TL;DR: Contingent capital: Valuation and risk Implications Under Alternative Conversion Mechanisms as mentioned in this paper, discusses alternative conversion and alternative conversion mechanisms in the context of Contingent Capital, and proposes an alternative conversion mechanism.
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Fluctuation theory for Lévy processes with completely monotone jumps
TL;DR: In this paper, it was shown that the space-time Wiener-Hopf factorization for Levy processes is complete Bernstein function of both the spatial and the temporal variable, and complete monotonicity of the distribution function of the supremum up to an independent exponential time.
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Pricing and Hedging Asian-Style Options in Energy
Fred Espen Benth,Nils Detering +1 more
TL;DR: The problem of pricing and hedging Asian-style options on energy with a quadratic risk criterion when trading in the underlying future is restricted is solved and there exists a unique solution if the future price process is a special semimartingale with bounded mean–variance tradeoff.
Journal ArticleDOI
Lévy processes, subordinators and crime modelling
TL;DR: In this article, the authors investigate some properties of Lévy processes in the context of subordinators, and propose an efficient implementation of the models by using high performance computing techniques.
Posted Content
Quasi-maximum likelihood estimation for cointegrated solutions of continuous-time state space models observed at discrete time points
TL;DR: In this article, a quasi-maximum likelihood (QML) estimation for the parameters of a cointegrated solution of a continuous-time linear state space model observed at discrete time points is investigated.