Improvement with compound Poisson-Geometric process risk model

The Poisson process in a classical risk model has some limitations,i.e.,the mean must be equal to its variance.This paper extends the Poisson process into a compound Poisson-Geometric process.The times of premium collection are regarded as a Poisson process,and the premium collected is considered as a random variable following exponential distribution.Therefore,the study extends a classical risk model.This paper will explain the significance of the improvement.With the calculation,the expressions of adjustment coefficient and ruin probability are obtained.Furthermore,the Lundeberg inequality for this risk model is derived.