Based On Time-series Model Of Ruin Theory

In the classics ruin model, the insurance premium collection rate is the constant, theinterest rate is the constant, the claim quantity is the random variable, these are the verystrong supposition, in this article alter to these conditions the time sequence model.So,The first part introduces the classic risk of the development of the theory, then tothe three di?erent areas (collection rate, the volume of claims, interest rates) on thecurrent development of the dependency structure, and pointed out that from this study:will be a number of time-series models introduced to the ruin theory, and also from thethree di?erent research ruin probability;In second part,some definition used in this article are description detailly;The third part is the core of this article,in this part, we use seven models of time-series to research ruin model in three aspects(collection rate, quantity of claims,interetrates),namely:The premium rate,claim quantity, the interest rate satisfies the AR(p) model sepa-rately, and may obtain the corresponding adjustment equation and the ruin probability.The premium rate,claim quantity, the interest rate satisfies the MA(q) model sepa-rately, and may obtain the corresponding adjustment factor equation ruin probability.The premium rate,claim quantity, the interest rate satisfies the ARMA(p,q) modelseparately, and may obtain the corresponding adjustment factor equation ruin probability.The premium rate,claim quantity, the interest rate satisfies the ARIMA(p,d,q) model separately, and may obtain the corresponding adjustment factor equation ruinprobability.The premium rate and claim quantity satisfies the periodic time sequence modelseparately, and may obtain the corresponding adjustment factor equation ruin probability.The premium rate and claim quantity satisfies the seasonal time sequence modelseparately, and may obtain the corresponding adjustment equation ruin probability The premium rate and claim quantity satisfies the trendy time series model sepa-rately,and may obtain the corresponding adjustment factor equation ruin probability.In the above ruin probability proof,has mainly applied the repetitive process and therice shoot method.In part four, 3 time-series model are made,ruin probability of time sequence modelmust be smaller than the classics ruin model.In part five, 3 dividend barrier(b,an + b,alog(n) + b) are simulated by computersoftware separately. We can obtain that the biggest optimal dividend of model is that theequation of dividend barrier is yn = b,but it is at the expense of the survival probability ;the middle one's is the equation of dividend barrier is yn = an + b, it is at the expense ofthe survival probability less than the first one's; the last one's is approximate in the fistone's,however,that is at the expense of the survival probability is the smallest.In short, in the time sequence of view, ruin probability is obtained about the premiumrate,claim quantity, the interest rate separately.Innovation: dependency structure models is replaced by time-series models com-pletely.So The new model can be very good close to the actual situation of insurancecompanies.And the ruin probability is easier to forecast.