Compound poisson processes, as modified by Ornstein-Uhlenbeck processes, Part II

Part I of this paper considered a collective risk model {R(t), 0≤t<∞} formed by a linear combination of four stochastic processes. The first process was a compound Poisson one which portrayed the claims. The other three processes were Ornstein-Uhlenbeck processes which served as models for deviations in assumptions about investment performance, operating expenses, and lapse expenses. We now remove the restriction that the claims process be a compound Poisson one. Furthermore, more general and meaningful values for the parameters in the Ornstein-Uhlenbeck processes are allowed. Basic properties of the R(t) process are presented. Probabilities of extreme deviations for the R(t) process are discussed, with several detailed examples.