Refined distributions for a multi-risk stochastic process

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Abstract
This paper considers a collective risk model formed linearly from four stochastic processes. The first process involves random sums of random variables, and portrays the insurance claims. The other three processes are Ornstein-Uhlenbeck processes which serve as models for the random deviations in assumptions about investment performance, operating expenses, and lapse expenses. The model presented earlier (Beekman 1975b, 1976) is improved by using both calendar and operational times. Ornstein-Uhlenbeck distributions for finite time periods are derived, and tables are furnished. Probabilities of extreme deviations for the multi-risk process are discussed. The examples in (Beekman 1975b, 1976) are reconsidered, and made more realistic by an improved treatment of the time variables.