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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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Generating Sparse Stochastic Processes Using Matched Splines
TL;DR: An off-the-grid algorithm is derived that generates arbitrarily close approximations of the target process of sparse stochastic processes that are solutions of linear ordinary differential equations driven by Lévy white noises.
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Assessing the Risks of Trading Strategies Using Acceptability Indices
TL;DR: In this article, the authors quantified the risks of trading strategies in incomplete markets and showed that using bid-ask prices compensates for the unhedgeable risk to an extent.
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Equivalent Measure Changes for Subordinate Diffusions
TL;DR: A subordinate diffusion is a Markov jump-diffusion or pure jump process obtained by time changing a diffusion process with an independent Levy or additive subordinator as discussed by the authors, which has found many applications in finance.
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Convex Order Properties of Discrete Realized Variance and Applications to Variance Options
TL;DR: In this article, the authors consider a square-integrable semimartingale with conditionally independent increments and symmetric jump measure, and show that the discrete realized variance dominates the quadratic variation in increasing convex order.
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The fractional Schr\"{o}dinger operator and Toeplitz matrices
TL;DR: In this paper, the authors identify the connection of the one-dimensional fractional Schr\"odinger operator with the truncated Toeplitz matrices and determine the asymptotic behaviour of the product of eigenvalues for the $\alpha$-stable symmetric laws by employing the Szeg\"o's strong limit theorem.