A Probability Model of Insurance for Random Indemnity and Random Discount and Some of its Results

In this paper, a stochastic process model of insurance, i.e. a double random model for random payment and random discounting is constructed firstly, and the properties of payment process are studied under the basic assumptions of the model. Using the theory of measure extension, we devolop the payment process into a random payment measure, aand give the measure representations for insurance and annuity, and give some famous actuarial formulas as well. Finally we obtain the present value moments of the random payment measure of Hoem model for the random interest rate Gauss process model, which is an extension of the results in 7.