The expected discounted penalty at ruin in the Erlang (2) risk process
In this paper, under the Erlang (2) risk process, we examine the expected discounted value of a penalty at ruin, which is considered as a function of the initial surplus. We first show that the expected discounted penalty function satisfies an integro-differential equation, and give its initial value, as well as its Laplace transform. We further prove that this function is twice differentiable, and satisfies a defective renewal equation. An explicit expression for the solution of this equation can be derived. The associated compound geometric distribution and "claim size" distribution are also studied.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Volume (Year): 72 (2005)
Issue (Month): 3 (May)
|Contact details of provider:|| Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description|
|Order Information:|| Postal: http://www.elsevier.com/wps/find/supportfaq.cws_home/regional|
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Dickson, David C. M. & Hipp, Christian, 2001. "On the time to ruin for Erlang(2) risk processes," Insurance: Mathematics and Economics, Elsevier, vol. 29(3), pages 333-344, December.
- Dufresne, Francois & Gerber, Hans U., 1988. "The surpluses immediately before and at ruin, and the amount of the claim causing ruin," Insurance: Mathematics and Economics, Elsevier, vol. 7(3), pages 193-199, October.
- Lin, X. Sheldon & Willmot, Gordon E., 1999. "Analysis of a defective renewal equation arising in ruin theory," Insurance: Mathematics and Economics, Elsevier, vol. 25(1), pages 63-84, September.
- Li, Shuanming & Garrido, Jose, 2004. "On ruin for the Erlang(n) risk process," Insurance: Mathematics and Economics, Elsevier, vol. 34(3), pages 391-408, June.
- Cai, Jun & Dickson, David C. M., 2002. "On the expected discounted penalty function at ruin of a surplus process with interest," Insurance: Mathematics and Economics, Elsevier, vol. 30(3), pages 389-404, June.
When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:72:y:2005:i:3:p:205-217. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei)
If references are entirely missing, you can add them using this form.