A note on Parisian ruin with an ultimate bankruptcy level for Lévy insurance risk processes
نویسندگان
چکیده
منابع مشابه
Gerber-Shiu distribution at Parisian ruin for Lévy insurance risk processes
Inspired by works of Landriault et al. [11, 12], we study the Gerber–Shiu distribution at Parisian ruin with exponential implementation delays for a spectrally negative Lévy insurance risk process. To be more specific, we study the so-called Gerber–Shiu distribution for a ruin model where at each time the surplus process goes negative, an independent exponential clock is started. If the clock r...
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We formulate the insurance risk process in a general Lévy process setting, and give general theorems for the ruin probability and the asymptotic distribution of the overshoot of the process above a high level, when the process drifts to −∞ a.s. and the positive tail of the Lévy measure, or of the ladder height measure, is subexponential or, more generally, convolution equivalent. Results of Asm...
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We examine discounted penalties at ruin for surplus dynamics driven by a general spectrally negative Lévy process; the natural class of stochastic processes which contains many examples of risk processes which have already been considered in the existing literature. Following from the important contributions of Zhou (2005) we provide an explicit characterization of a generalized version of the ...
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In this note we give, for a spectrally negative Lévy process, a compact formula for the Parisian ruin probability, which is defined by the probability that the process exhibits an excursion below zero which length exceeds a certain fixed period r. The formula involves only the scale function of the spectrally negative Lévy process and the distribution of the process at time r.
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We describe a fast simulation framework for simulating small ruin probabilities in insurance risk processes with subexponential claims. Naive simulation is inefficient since the event of interest is rare, and special simulation techniques like importance sampling need to be used. An importance sampling change of measure known as sub-exponential twisting has been found useful for some rare event...
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ژورنال
عنوان ژورنال: Statistics & Probability Letters
سال: 2016
ISSN: 0167-7152
DOI: 10.1016/j.spl.2016.02.018