Occupation times of spectrally negative lévy processes with applications
TLDR
In this paper, the Laplace transform of occupation times of spectrally negative Levy processes is computed in terms of the so-called scale functions of the spectral negative Levy process and its Laplace exponent.About:
This article is published in Stochastic Processes and their Applications.The article was published on 2011-11-01 and is currently open access. It has received 95 citations till now. The article focuses on the topics: Laplace transform & Wiener process.read more
Citations
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Occupation times of intervals until first passage times for spectrally negative Lévy processes
TL;DR: In this paper, the authors identify Laplace transforms of occupation times of intervals until first passage times for spectrally negative Levy processes and derive analytical identities for scale functions of the process.
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Exit identities for Lévy processes observed at Poisson arrival times
TL;DR: For a spectrally one-sided Levy process, this paper extended various two-sided exit identities to the situation when the process is only observed at arrival epochs of an independent Poisson process.
Journal ArticleDOI
An Insurance Risk Model with Parisian Implementation Delays
TL;DR: In this paper, the authors consider a variant of the event ruin for a Levy risk process, where the surplus process is allowed to spend time under a pre-specified default level before ruin is recognized.
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Ruin probability with Parisian delay for a spectrally negative Lévy risk process
Irmina Czarna,Zbigniew Palmowski +1 more
TL;DR: In this paper, the Parisian ruin probability, which arises when the surplus process stays below 0 longer than a fixed amount of time ζ > 0, is analyzed. And the authors derive an expression for the Parisians ruin probability in terms of quantities that can be calculated explicitly in many models.
Journal ArticleDOI
Exit identities for L\'evy processes observed at Poisson arrival times
TL;DR: For a spectrally one-sided L 'evy process, this paper extended various two-sided exit identities to the situation when the process is only observed at arrival epochs of an independent Poisson process.
References
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Book
Brownian Motion and Stochastic Calculus
TL;DR: In this paper, the authors present a characterization of continuous local martingales with respect to Brownian motion in terms of Markov properties, including the strong Markov property, and a generalized version of the Ito rule.
Book
Diffusion Processes and their Sample Paths
Kiyosi Itô,Henry P. McKean +1 more
TL;DR: In this article, the authors consider the problem of approximating the Brownian motion by a random walk with respect to the de Moivre-laplace limit theorem and show that it is NP-hard.
Book
Introductory Lectures on Fluctuations of Lévy Processes with Applications
TL;DR: In this paper, the authors present decompositions of the paths of Levy processes in terms of their local maxima and an understanding of their short-and long-term behaviour.
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.
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Brownian excursions and parisian barrier options
TL;DR: In this article, the authors study a new variant of the so-called barrier option: a down-and-out barrier option becomes worthless as soon as a barrier is reached, whereas a down and-out Parisian barrier option is lost by the owner if the underlying asset reaches a prespecified level and remains constantly below this level for a time interval longer than a fixed number.