2019
DOI: 10.1007/978-3-030-04161-8_21
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Parisian Excursion Below a Fixed Level from the Last Record Maximum of Lévy Insurance Risk Process

Abstract: This paper presents some new results on Parisian ruin under Lévy insurance risk process, where ruin occurs when the process has gone below a fixed level from the last record maximum, also known as the high-water mark or drawdown, for a fixed consecutive periods of time. The law of ruin-time and the position at ruin is given in terms of their joint Laplace transforms. Identities are presented semi-explicitly in terms of the scale function and the law of the Lévy process. They are established using recent develo… Show more

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Cited by 5 publications
(14 citation statements)
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References 22 publications
(22 reference statements)
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“…Relying on a temporal approximation approach (e.g., Li et al[17]), the proposed methodology allows for a unied treatment of processes with bounded and unbounded variation paths whereas these two cases used to be treated separately (e.g., Yin and Yuen [30]). In particular, we extend the results of Landriault et al [14] and Surya [28]. We later analyze certain limiting cases of our main results where consistency with some known drawdown results in the literature will be shown.…”
supporting
confidence: 80%
“…Relying on a temporal approximation approach (e.g., Li et al[17]), the proposed methodology allows for a unied treatment of processes with bounded and unbounded variation paths whereas these two cases used to be treated separately (e.g., Yin and Yuen [30]). In particular, we extend the results of Landriault et al [14] and Surya [28]. We later analyze certain limiting cases of our main results where consistency with some known drawdown results in the literature will be shown.…”
supporting
confidence: 80%
“…which recovers Theorem 2.1 of [26]. It can then be checked via a change of measure that Proposition 2.3 of [26] can also be recovered from our Theorem 4.2.…”
Section: Resultsmentioning
confidence: 55%
“…Notice that to compute the draw-down Parisian ruin probability (see Remark 4.1), we only need the expression for r := (0) r . To find the Laplace transform associated to the two-sided exit solution (26), the kth moment of dividends (see Theorem 4.4), or the potential measure of X (see Theorem 4.3) involving the draw-down Parisian ruin time, we also need the expression for (q) r . If we want to compute the probability density of the draw-down Parisian ruin time, we must first use the expression for (q) r to compute the right-hand side of (30), then numerically invert it using the algorithms in [7] or the method of Fourier series expansion proposed by [23], which has been proven to be an efficient method for the numerical inversion of Laplace transforms.…”
Section: Small Claims: Brownian Motionmentioning
confidence: 99%
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