Some results of ruin probability for the classical risk process
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.
scientific article; zbMATH DE number 2069808