Description: The initial risk reserves in collective risk models vary according to the underlying claim distribution, and a suitable level of ruin probability. A thorough analysis of the needed initial surplus for various ruin probability levels is provided in eight meaningful examples. The claim distributions are drawn from various fields of insurance, including property damage and liability insurance.

Description: The subject of this paper is a mathematical model for insurance company risks formed by a linear combination of four stochastic processes recognizing claim patterns, investment performance assumptions, operating expenses and lapse expenses. A discussion of the paper follows. From Transactions of Society of Actuaries 1978, Vol. 30.

Description: This paper presents a model is which can be used for certain annuities when interest rates and future lifetimes are random. These can be used in determining contingency reserves for possible adverse interest and mortality experience for collections of life annuity contracts. Certain boundary crossing probabilities for the stochastic process component of the model are obtained. From Actuarial Research Clearing House 1991, VOL. 1.