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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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Truncated Realized Covariance when prices have infinite variation jumps
TL;DR: In this article, the authors show that the convergence of the Truncated Realized Covariance (TRC) to the Integrated Covariation between the Brownian parts of two semimartingales is heavily influenced by the presence of infinite activity jumps with infinite variation (iV), through both the degree of dependence and the jump activity indices of the two small jumps processes.
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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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.
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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.
Journal ArticleDOI
Inhomogeneous Random Evolutions: Limit Theorems and Financial Applications
Nelson Vadori,Anatoliy Swishchuk +1 more
TL;DR: In this paper, the authors introduce and present some properties of inhomogeneous random evolutions (IHRE), and prove weak law of large numbers and central limit theorems for IHRE.
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.