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Volume 28, Issue 4
A Joint Density Function in Phase-Type (2) Risk Model

Huai Xu & Ling Tang

Commun. Math. Res., 28 (2012), pp. 349-358.

Published online: 2021-05

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  • Abstract

In this paper, we consider a Gerber-Shiu discounted penalty function in Sparre Andersen risk process in which claim inter-arrival times have a phase-type (2) distribution, a distribution with a density satisfying a second order linear differential equation. By conditioning on the time and the amount of the first claim, we derive a Laplace transform of the Gerber-Shiu discounted penalty function, and then we consider the joint density function of the surplus prior to ruin and the deficit at ruin and some ruin related problems. Finally, we give a numerical example to illustrate the application of the results.

  • Keywords

Gerber-Shiu discounted penalty function, phase-type (2) distribution, surplus prior to ruin, deficit at ruin.

  • AMS Subject Headings

60P05, 60H10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-28-349, author = {Xu , Huai and Tang , Ling}, title = {A Joint Density Function in Phase-Type (2) Risk Model}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {28}, number = {4}, pages = {349--358}, abstract = {

In this paper, we consider a Gerber-Shiu discounted penalty function in Sparre Andersen risk process in which claim inter-arrival times have a phase-type (2) distribution, a distribution with a density satisfying a second order linear differential equation. By conditioning on the time and the amount of the first claim, we derive a Laplace transform of the Gerber-Shiu discounted penalty function, and then we consider the joint density function of the surplus prior to ruin and the deficit at ruin and some ruin related problems. Finally, we give a numerical example to illustrate the application of the results.

}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/19036.html} }
TY - JOUR T1 - A Joint Density Function in Phase-Type (2) Risk Model AU - Xu , Huai AU - Tang , Ling JO - Communications in Mathematical Research VL - 4 SP - 349 EP - 358 PY - 2021 DA - 2021/05 SN - 28 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cmr/19036.html KW - Gerber-Shiu discounted penalty function, phase-type (2) distribution, surplus prior to ruin, deficit at ruin. AB -

In this paper, we consider a Gerber-Shiu discounted penalty function in Sparre Andersen risk process in which claim inter-arrival times have a phase-type (2) distribution, a distribution with a density satisfying a second order linear differential equation. By conditioning on the time and the amount of the first claim, we derive a Laplace transform of the Gerber-Shiu discounted penalty function, and then we consider the joint density function of the surplus prior to ruin and the deficit at ruin and some ruin related problems. Finally, we give a numerical example to illustrate the application of the results.

Xu , Huai and Tang , Ling. (2021). A Joint Density Function in Phase-Type (2) Risk Model. Communications in Mathematical Research . 28 (4). 349-358. doi:
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