Research Of The Risk Models Ruin Probability And Absolute Ruin Probability With Investment

Firstly, a dependent risk model with investment and diffusion under refundingprocess is discussed, where the arrival of the term policies follows a poissonprocess,and the occurrence of the claim and refunding happen as the p thinningprocess and the q thinning process of the arrival process respectively.For thismodel, the expression and an upper bound of the eventual ruin probability arederived by using the martingale method.Various trends of the upper bound of ruinprobability are simulated analytically along with changing the investment,premiumsize, claim size and refunding size, and the results are heuristic to operate theinsurance business.On the other hand, built in proportion to share out bonus strategy consideringinvesting and lending absolute bankruptcy model to study the model of Gerber-Shiuexpect the discount fine function of meet the integral differential equation, andanalyzes the amount of the claim obeys index distribution and obtains expect thediscount fine function of the specific meet integral differential equations areobtained, and get the differential integral equation solution, and the promotion of theclassical risk model relevant conclusion.Finally, on the one hand, consider linear share out bonus strategy withinvestment and interfere with the absolute risk of model, it is concluded that theaccord with the model of Gerber-Shiu function of integral differential equation, giveclaim amount subject to index the absolute ruin probability distribution, make anexample analysis of different investment amount, loan interest rates to ruinprobability are the effect of actual business to make a significant guidance.