The Equivalence of Two Disctete Risk Models
LIU Xiangdong,YANG Xiangqun (Department of Mathematics,Hunan Normal University, Changsha 410081,China)
The insurance company must pay the insureds insurance calms if accidents occur.Let us consider the integer time i, i=0,1,2,3,..., we suppose that the company pays only at time i even sevaral accidents occur in time interval(i1,i],so we may consider one accident or no accident at time i.Up to time n,the total of insurance calms may count in two models.The first model is said to be the type of A model:the company pays immediately if accident occurs at some time,the ith calm is a random variable ξ i,i=1,2,3,...,which are (0,+∞)valued,independent each other,and have same distribution,the total of insurance calms up to time n is ,so we may consider one accident or no accident at time i.Up to time n,the total of insurance calms may count in two models.The first model is said to be the type of A model:the company pays immediately if accident occurs at some time,the ith calm is a random variable ξ i,i=1,2,3,...,which are (0,+∞)valued,independent each other,and have same distribution,the total of insurance calms up to time n is N(n)i=1ξ i,where N(n) is the sum of numbers of accidents occured up to time n.The second model is said to be the type of B model:the company pays at each time i,random variable X i is the insurance calm at time i,i=1,2,3,...,which are [0,+∞)valued,independent each other,and have same distribution,the total of insurance calms up to time n is [DD(]ni=1X i.In this paper we proved the equivalence of two models rigorously using theory of stochastic process.


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