Volume 29, Issue 1
A Joint Density Function in the Renewal Risk Model

Huai Xu & Ling Tang

Commun. Math. Res., 29 (2013), pp. 88-96.

Published online: 2021-05

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  • Abstract

In this paper, we consider a general expression for $ϕ(u, x, y)$, the joint density function of the surplus prior to ruin and the deficit at ruin when the initial surplus is $u$. In the renewal risk model, this density function is expressed in terms of the corresponding density function when the initial surplus is 0. In the compound Poisson risk process with phase-type claim size, we derive an explicit expression for $ϕ(u, x, y)$. Finally, we give a numerical example to illustrate the application of these results.

  • Keywords

deficit at ruin, surplus prior to ruin, phase-type distribution, renewal risk model, maximal aggregate loss.

  • AMS Subject Headings

60P05, 60H10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-29-88, author = {Xu , Huai and Tang , Ling}, title = {A Joint Density Function in the Renewal Risk Model}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {29}, number = {1}, pages = {88--96}, abstract = {

In this paper, we consider a general expression for $ϕ(u, x, y)$, the joint density function of the surplus prior to ruin and the deficit at ruin when the initial surplus is $u$. In the renewal risk model, this density function is expressed in terms of the corresponding density function when the initial surplus is 0. In the compound Poisson risk process with phase-type claim size, we derive an explicit expression for $ϕ(u, x, y)$. Finally, we give a numerical example to illustrate the application of these results.

}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/19031.html} }
TY - JOUR T1 - A Joint Density Function in the Renewal Risk Model AU - Xu , Huai AU - Tang , Ling JO - Communications in Mathematical Research VL - 1 SP - 88 EP - 96 PY - 2021 DA - 2021/05 SN - 29 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cmr/19031.html KW - deficit at ruin, surplus prior to ruin, phase-type distribution, renewal risk model, maximal aggregate loss. AB -

In this paper, we consider a general expression for $ϕ(u, x, y)$, the joint density function of the surplus prior to ruin and the deficit at ruin when the initial surplus is $u$. In the renewal risk model, this density function is expressed in terms of the corresponding density function when the initial surplus is 0. In the compound Poisson risk process with phase-type claim size, we derive an explicit expression for $ϕ(u, x, y)$. Finally, we give a numerical example to illustrate the application of these results.

Huai Xu & Ling Tang. (2021). A Joint Density Function in the Renewal Risk Model. Communications in Mathematical Research . 29 (1). 88-96. doi:
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