随机赔偿、随机折现下的保险概率模型及若干结果

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

本文首先构造了保险的随机过程模型，即随机赔偿和随机折现的双随机模型．运用测度扩张理论将赔偿过程发展为随机赔偿恻度，在模型的基本假定之下研究赔偿过程的性质，给出保险和年金的测度表示以及诸多精算公式．最后针对随机利率的Gauss过程模型得到Hoem模型随机赔偿测度的现值矩发展了［7］中的主要结果．

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].