Alarm System For Reinsurance In Compound Binomial Model With Constant Dividend Barrier

For insurance companies,it is a good idea for risk management to establish an alarm system before ruin.The size of the future risk depends on the accumulation of premiums and the claims of insurance companies with a given initial surplus.In this paper,we design an alarm system for reinsurance in compound binomial model with constant dividend barrier,which will give a risk alarm under given conditions at some periodic detection time and prompt purchasing proportional reinsurance within this period to reduce the possibility of ruin.In order to test and verify the effectiveness of the alarm system,we compare surplus values and discounted values of dividends with and without an alarm system.We obtain the following conclusion: an alarm system for reinsurance can reduce initial surplus,effectively relieve the pressure of risk and raise the value of company.In addition,The latter part of this paper,we use the firefly algorithm to solve the unknown parameters in the warning system and model,and get the optimal cumulative dividend discount value.In the first chapter of this paper is the introduction part,which mainly introduces the relevant research background and research status,then leads to the research methods and innovation of this paper,and finally makes a simple description of the overall framework.In the second chapter is preparatory knowledge.In this chapter,we give a detailed description of the basic knowledge involved in the paper.In the third chapter,we first analyze the law of bankruptcy time T from the distribution of claims and the change of initial surplus.Then we use bankruptcy time T to define the warning time point.Finally,we generalize a series of early warning detection points from a single early warning time point to construct the whole reinsurance early warning system.In the fourth chapter,we introduce the constant dividend boundary into the earnings model with warning system,and measure the value of the company through the cumulative dividend discount value(value function).This paper analyzes the influence of various parameters in the warning system on the cumulative dividend discount value,and shows that the earnings model with the warning system can improve the value of the company and the ability of anti risk through data comparison.In the fifth chapter,the equation of the optimal value function is given.The optimal value function is calculated by using the firefly algorithm,and the corresponding parameters are obtained.Finally,a numerical example is given based on the stochastic simulation method,which shows that the reinsurance early warning system has a positive effect on the whole earnings process.The last part is a brief summary of the ideas and results of the whole article,then points out the significance of this study and the issues to be considered in the future.