The mixed negative binomial process risk model with small claims stochastic process and ruin probability

If the random variable changes with time, we can consider it a stochastic process. The stochastic claims process is particularly important in insurance, where the frequency of claims is a random variable. Classical risk models typically assume that the number of claims by insurance companies follows an (a, b, 0) type distribution. In practice, however, the number of claims is often an over-dispersed or heavy-tailed phenomenon. To compensate for this deficiency, mixed distributions have been proposed. This article discusses the lapse probability of a general compound mixed negative binomial small claims process risk model based on a negative binomial mixture distribution.