Generalized Polya-Aeppli Process and Its Applications in Risk Modelling and Analysis
Journal Title: IOSR journal of Business and Management - Year 2018, Vol 20, Issue 10
Abstract
In this paper, we introduce a new compound Poisson process with truncated negative binomial compounding distribution, which we will call as the Generalized Polya-Aeppli Process. We derived expressions for its probability mass function (p.m.f) and discuss several properties. We develop a new risk model with the Generalized Polya-Aeppli process as the counting process. Also, we derived the joint distribution of the time to ruin and deficit at the time of ruin. The differential equation of the ruin probability is given. As an example, we consider the case where the claim size follows the exponential distribution. We derive distributions of aggregate claims and gain (loss) from the Generalized Polya-Aeppli risk model and compute the stop loss premium.
Authors and Affiliations
Shalitha Jacob, K. K. Jose
Keywords
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- EP ID EP412990
- DOI 10.9790/487X-2010012435.
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