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Old and New Examples of Scale Functions for Spectrally Negative Levy Processes
, 2007We give a review of the state of the art with regard to the theory of scale functions for spectrally negative Levy processes. From this we introduce a general method for generating new families of scale functions.
F. Hubalek, E. Kyprianou
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Draw-down Parisian ruin for spectrally negative Lévy processes
Advances in Applied Probability, 2019Draw-down time for a stochastic process is the first passage time of a draw-down level that depends on the previous maximum of the process. In this paper we study the draw-down-related Parisian ruin problem for spectrally negative Lévy risk processes ...
Wenyuan Wang, Xiaowen Zhou
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Last exit time until first exit time for spectrally negative Lévy processes
Journal of Applied ProbabilityWe study the last exit time that a spectrally negative Lévy process is below zero until it reaches a positive level b, denoted by $g_{\tau_b^+}$ .
Xiaofeng Yang, J. M. Pedraza, Bin Li
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Approximation and estimation of scale functions for spectrally negative Lévy processes
Journal of Applied ProbabilityThe scale function plays a significant role in the fluctuation theory of Lévy processes, particularly in addressing exit problems. However, its definition is established through the Laplace transform, which generally lacks an explicit representation ...
Haruka Irie, Yasutaka Shimizu
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Dividend payments until draw-down time for risk models driven by spectrally negative Lévy processes
Communications in statistics. Simulation and computation, 2020In this paper, a risk model driven by spectrally negative Lévy processes is considered where dividends until a general draw-down time are paid under a constant barrier strategy.
Zhang Liu, Ping Chen
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Occupation Times of Intervals Until Last Passage Times for Spectrally Negative Lévy Processes
, 2016In this paper, we derive the Laplace transform of occupation times of intervals until last passage times for spectrally negative Lévy processes. Motivated by [2], the last passage times before an independent exponential variable are investigated.
C. Cai, Bo-Yan Li
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