A Risk Model With Proportional Reinsurance

The situation described by the classical risk model is too idealistic, leading to limitations in the practical application. Insurance companies continued access to capital by selling insurance policies, claims also occur. Strictly speaking, when the insurance company’s surplus drops below0,we think the insurance companies "bankrupt", but generally the actual situation is when the surplus of the insurance company under a limit that insurance company has "bankruptcy" so as to facilitate timely to give early warning to take appropriate measures to manage the risk. Of course, sometimes when the policy is sold insurance company already adopted some measures to diversify the risk, usually we use reinsurance. This paper is to establish a risk model with dependent proportional reinsurance to discuss.This paper consists of two parts, The first part includes the first chapter and the second chapter, in the first chapter mainly introduces the development of L-C classical risk model in recent years and this paper’s framework.The second chapter introduces some prior knowledge about the random point process, sparse process, martingale, reinsurance and so on.The second part is from Chapter3to Chapter6.Based on the risk model in the text [31], the paper consider proportional reinsurance bankruptcy lower limit is introduced in chapter4.Chapter5establishes and deeps risk model based on Chapter4, introducing the composite negative binomial distribution. Considering part of the policy obeys the Poisson process, and another part of the policy of income and claims follow a negative binomial distribution.The model introduces random interference in chapter6, and obtain the corresponding conclusion.