Perturbed Risk Model Under Non-linear Dividend Barrier

In order to reduce the loss of the risk in future, the insurance is proposed, however, thegeneral risk models have been unable to accurately describe the reality of the insurance company,for example, we have to take into account the dividend strategy, therefore, research on risk modelwith bonus boundaries is increasingly concerned.This paper first describes the background and status of the insurance industry, then proposesa new risk model based on classical risk model: Consider market factors under the dividendstrategy with nonlinear boundary, join the disturbance term, the risk model is more close to thedaily operating conditions of the insurance company, we give the probability of survival and theGerber-Shiu discounted penalty function under this model, finally we introduce the concept ofabsolute bankruptcy and give the probability of survival and the Gerber-Shiu discounted penaltyfunction of this model.