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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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Dissertation
Mortality linked derivatives and their pricing
TL;DR: In this article, the authors proposed a model-independent pricing method for catastrophic mortality bonds by exploiting the theory of comonotonicity and derived general price bounds for GAOs under the most generalized modeling framework where both interest rate and mortality risk are stochastic and correlated.
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On Weak Solutions of SDEs with Singular Time-Dependent Drift and Driven by Stable Processes
TL;DR: In this article, the authors studied weak solutions for the following type of stochastic differential equations: dXt = dSt + b(s + t,Xt)dt, t ≥ 0, X0 = x, where (s,x) ∈ ℝ+ × ℜd is the starting point, b : Å+ ×ℝd → ℘d is measurable, and S = (St)t≥0 is a d-dimensional centered α-stable process with index α ∈ (1,
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Strong laws at zero for trimmed Lévy processes
TL;DR: In this paper, the authors studied the convergence of a Levy process with extreme values removed, and gave necessary and sufficient conditions for the a.s. convergence of the Levy process under natural conditions on the norming functions.
Journal ArticleDOI
Explicit solution of an inverse first-passage time problem for L\'{e}vy processes and counterparty credit risk
M. H. A. Davis,M. R. Pistorius +1 more
TL;DR: In this article, the authors consider a version of the inverse first-passage time problem where the barrier is fixed at zero and the problem is to find an initial distribution and a time-change $I$ such that for the time-changed process $X\circ I$ the IFPT problem is solved by a constant barrier at the level zero.
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Error bounds for small jumps of Lvy processes
TL;DR: In this paper, the authors derived bounds for the errors generated by truncating or replacing small jumps by a Brownian motion with the same variance, and showed that these two types of approximations are both error-prone.
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.