The Ruin Probability of the Compound Negative Binomial Risk Model with a Completely Stochastic Premium

摘要

Based on the compound negative binomial risk model, this paper attempts to construct a compound negative binomial risk model with a completely stochastic premium where the premium of every policy and the number of insure charges at per unit time are random variables. Applying discrete martingale theory, the paper explores some properties of a compound negative binomial risk model with a completely stochastic premium. Consequently, it proves the formula of ultimate ruin probability and the Lundberg inequality.