Some results of ruin probability for the classical risk process
type: Item
instance of: scholarly article
title: Some results of ruin probability for the classical risk process
zbMATH Open document ID: 1103.91365
DOI: 10.1155/S1173912603000130
author: Yuanjiang He
author: Xucheng Li
author: John Zhang
published in: Journal of Applied Mathematics and Decision Sciences
publication date: 2004-05-27T00:00:00Z
full work available at URL: https://eudml.org/doc/126862
review text: Summary: The computation of ruin probability is an important problem in the collective risk theory. It has applications in the fields of insurance, actuarial science, and economics. Many mathematical models have been introduced to simulate business activities and ruin probability is studied based on these models. Two of these models are the classical risk model and the Cox model. In the classical model, the counting process is a Poisson process and in the Cox model, the counting process is a Cox process. Thorin (1973) studied the ruin probability based on the classical model with the assumption that random sequence followed the \(\Gamma\) distribution with density function \(f(x)=\frac{x^{\frac 1\beta -1}}{\beta^{\frac 1\beta}\Gamma(1/\beta)}e^{-\frac x\beta}, x> 0\), where \(\beta > 1.\) This paper studies the ruin probability of the classical model where the random sequence follows the \(\Gamma\) distribution with density function \(f(x)=\frac {\alpha^n}{\Gamma (n)}x^{n-1}e^{-\alpha x},x>0\) where \(\alpha>0\) and \(n\geq 2\) s a positive integer. An intermediate general result is given and a complete solution is provided for \(n=2\). Simulation studies for the case of \(n=2\) is also provided.
Mathematics Subject Classification ID: 91B30
zbMATH DE Number: 2069808
MaRDI profile type: Publication
OpenAlex ID: W2018644664
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description: scientific article; zbMATH DE number 2069808