Journal of Applied Mathematics and Decision Sciences
Volume 7 (2003), Issue 3, Pages 133-146
doi:10.1155/S1173912603000130
Some results of ruin probability for the classical risk process
1Department of Statistics Science, Zhongshan University, Ganglion, 510275 PR, China
2Department of Mathematics, Indiana University of Pennsylvania, Indiana 15705, PA, USA
Copyright © 2003 He Yuanjiang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
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 Γ distribution with density function f(x)=x1β−1β1βΓ(1/β)e−xβ, x>0, where β>1. This paper studies the ruin probability of the classical model where the random sequence follows the Γ distribution with density function f(x)=αnΓ(n)xn−1e−αx, x>0, where α>0 and n≥2 is 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.