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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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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.
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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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On the dynamics of semimartingales with two reflecting barriers
Mats Pihlsgård,Peter W. Glynn +1 more
TL;DR: In this article, a semimartingale X which is reflected at an upper barrier T and a lower barrier S, where T is bounded away from S, is considered and a relationship in terms of stochastic integrals linking the reflected process and the local times at the respective bathers to X, S, and T is derived.
Journal ArticleDOI
Fractional calculus and pathwise integration for Volterra processes driven by Lévy and martingale noise
TL;DR: In this article, a pathwise integration for Volterra processes driven by Lévy noise or martingale noise is presented, which is based on fractional calculus and in this there is a bridging of the stochastic and deterministic techniques.
Portfolio Optimization and Stochastic Control under Transaction Costs
TL;DR: In this article, the authors considered a general menu cost problem with partially controlled regime switching, general multidimensional running cost problems and the maximization of long-term growth rates in incomplete markets.
Posted Content
Pricing and Hedging Options in Energy Markets Using Black-76
TL;DR: In this paper, it was shown that the prices of options on forwards in commodity markets converge to the Black-76 formula when the short-term variations of the logarithmic spot price are a stationary Ornstein-Uhlenbeck process and the long-term changes are following a drifted Brownian motion.
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The Microstructure of Stochastic Volatility Models with Self-Exciting Jump Dynamics
Ulrich Horst,Wei Xu +1 more
TL;DR: In this paper, the authors provide a general probabilistic framework within which they establish scaling limits for a class of continuous-time stochastic volatility models with self-exciting jump dynamics.