I-Delaporte process and applications
M.D. Lazarova and
L.D. Minkova
Mathematics and Computers in Simulation (MATCOM), 2017, vol. 133, issue C, 135-141
Abstract:
In this paper we introduce a mixed Pólya–Aeppli process with shifted gamma mixing distribution and call it an Inflated-parameter Delaporte process (I-Delaporte process). We derive the probability mass function, moments and some basic properties. Then we define the process as a pure birth process and derive differential equations for the probabilities. As application, we consider a risk model in which the claim counting process is the defined I-Delaporte process. For the defined risk model we derive the joint distribution of the time to ruin and the deficit at ruin as well as the ruin probability. We discuss in detail the particular case of exponentially distributed claims.
Keywords: Mixed distributions; Pure birth process; Delaporte process; Ruin probability (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations:
Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378475415002608
Full text for ScienceDirect subscribers only
Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
HTML/Text
Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:133:y:2017:i:c:p:135-141
DOI: 10.1016/j.matcom.2015.12.003
Access Statistics for this article
Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens
More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier
Bibliographic data for series maintained by Catherine Liu ().