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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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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.
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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.
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On non-existence of global solutions to a class of stochastic heat equations
Mohammud Foondun,Rana D. Parshad +1 more
TL;DR: In this paper, the authors consider nonlinear parabolic SPDEs and show that the second moment of their solutions blow up in finite time under some suitable conditions on the parameters of these SPDEs.
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The best gain-loss ratio is a poor performance measure
Sara Biagini,Mustafa Ç. Pınar +1 more
TL;DR: It is shown that the best market gain- loss ratio in the presence of a random endowment is an acceptability index and its dual representation for general probability spaces proves that the (best) gain-loss is a poor performance measure.
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.