Analysis Of A Risk Model With Stochastic Premiums Based On NGINAR(1) Process

In this thesis,we use integer-valued autoregressive(NGINAR(1))process based on negative Binomial thinning operator to describe the dynamic relationship of the premium collection numbers(could be understood as the numbers of the policies)in different periods?and propose a new dependent risk model,i.e.,in which Ut denotes the surplus of the insurance company until period t,and U0=u is the initial capital.Xt and Yt represent the premium income and claim amount during period t,respectively.Moreover,the premium collection number during period t is supposed to satisfy the following recursive equation:Nt=?*Nt-1+?t,t=2,3,…,where the negative Binomial thinning operator is defined asin which {Wt,m,t=1,2,…,m=1,2.…} is an i.i.d.Geometric random variable array.We name(1)a risk model with stochastic premiums based on NGINAR(1)process.Our model has an intuitive explanation in practice:the insurance policies of the insurance company in the period t consists of two parts,some are the regular customers who insured in period t-1 and new customers introduced by the regular customers,denoted by ?*Nt-1.the rest are the people who purchase insurance in period t by other ways,denoted by ?t.For risk model(1),we derive some probabilistic and statistical properties,give the equation satisfied by the adjustment coefficient,obtain the Lundberg approximation formula of ruin probability,discuss the effects of parameter ? on ruin probability,and illustrate the main results by numerical simulations.Our conclusion shows that it is very important for insurance companies to improve product quality,service level and customer experience,because these measures are of great significance to reduce customer churn,attract new customers and lower ruin risk.