Some results of ruin probability for the classical risk process

[摘要] The computation of ruin probability is an important problem in the collectiverisk theory. It has applications in the fields of insurance, actuarial science, andeconomics. Many mathematical models have been introduced to simulate business activitiesand ruin probability is studied based on these models. Two of these modelsare the classical risk model and the Cox model. In the classical model, the countingprocess is a Poisson process and in the Cox model, the counting process is a Coxprocess. Thorin (1973) studied the ruin probability based on the classical model withthe assumption that random sequence followed theΓdistribution with density functionf(x)=x1β−1β1βΓ(1/β)e−xβ,x>0, whereβ>1. This paper studies the ruin probability of the classical model where the random sequence follows theΓdistribution with density functionf(x)=αnΓ(n)xn−1e−αx,x>0, whereα>0andn≥2is a positive integer. An intermediate general result is given and a complete solution is provided forn=2. Simulation studies for the case ofn=2is also provided.

[学科分类] 自然科学（综合）