On the occupation times in a delayed Sparre Andersen risk model with exponential claims

Can Jin, Shuanming Li, Xueyuan Wu

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2 Citations (Scopus)

Abstract

In this paper, we study the joint Laplace transform of the occupation times in disjoint intervals until ruin in a delayed Sparre Andersen risk model with general inter-claim times and exponential claims. We extend the transformation method in the literature and apply the theoretical fluctuation techniques to derive an explicit expression of the joint Laplace transform under consideration. Further, with the presence of a constant dividend barrier, we derive explicit expressions for the Laplace transforms of the time of ruin and the non-dividend paying duration, namely the total length of non-dividend paying periods prior to ruin. This quantity is of practical interest but has not been studied in the literature to date. Within this paper, all of the Laplace transforms are expressed in terms of scale functions associated with the given spectrally negative Lévy process. Numerical examples are also provided at the end of this paper regarding the Laplace transform of the non-dividend paying duration to illustrate how the distribution of this occupation time behaves in response to varying parameters and the impact of delay on the occupation times comparing with an ordinary Sparre Andersen risk model.

Original languageEnglish
Pages (from-to)304-316
Number of pages13
JournalInsurance: Mathematics and Economics
Volume71
DOIs
Publication statusPublished - 1 Nov 2016

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Occupation Time
Laplace transform
Scale Function
Model
Dividend
Disjoint
Risk model
Fluctuations
Numerical Examples
Interval

Cite this

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abstract = "In this paper, we study the joint Laplace transform of the occupation times in disjoint intervals until ruin in a delayed Sparre Andersen risk model with general inter-claim times and exponential claims. We extend the transformation method in the literature and apply the theoretical fluctuation techniques to derive an explicit expression of the joint Laplace transform under consideration. Further, with the presence of a constant dividend barrier, we derive explicit expressions for the Laplace transforms of the time of ruin and the non-dividend paying duration, namely the total length of non-dividend paying periods prior to ruin. This quantity is of practical interest but has not been studied in the literature to date. Within this paper, all of the Laplace transforms are expressed in terms of scale functions associated with the given spectrally negative L{\'e}vy process. Numerical examples are also provided at the end of this paper regarding the Laplace transform of the non-dividend paying duration to illustrate how the distribution of this occupation time behaves in response to varying parameters and the impact of delay on the occupation times comparing with an ordinary Sparre Andersen risk model.",
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On the occupation times in a delayed Sparre Andersen risk model with exponential claims. / Jin, Can; Li, Shuanming; Wu, Xueyuan.

In: Insurance: Mathematics and Economics, Vol. 71, 01.11.2016, p. 304-316.

Research output: Contribution to journalArticleResearchpeer-review

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AU - Wu, Xueyuan

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