The Compound Poisson Risk Model With Constant Interest Rate Under A Mixed Dividend Strategy

Risk theory is the core of actuarial mathematics research.It studies the operating characteristics of insurance companies by studying random risk models in the insurance industry.In recent years,with the development of society and the progress of the times,insurance companies have not only limited the management of funds to simple fund storage,but have chosen to invest in various projects to obtain higher returns.Investments are often accompanied by risks,so effective predicting the risks and benefits of investment is particularly important for insurance companies' capital management and stable operations.Based on the compound Poisson risk model under the mixed dividend strategy of Zhang and Han(2017),this paper considers the impact of interest rate factors on the risk assets of insurance companies under this model,that is,proposes a mixed dividend strategy with constant interest rate Poisson risk model,this paper mainly discusses Gerber-Shiu's expected discounted penalty function and expected discounted dividend function before bankruptcy.The paper first gives the expressions of Gerber-Shiu's expected discounted penalty function and expected discounted dividend function.Based on this basic expression,in the case of 0?u<b and u? b about the initial capital u and the threshold b,this paper uses update theory to derive and obtain the specifics of Gerber-Shiu's expected discounted penalty function,expected discounted dividend function,and the corresponding integral differential equation.In particular,when claims follows an exponential distribution,this paper derives the exact expressions of Gerber-Shiu's expected discounted penalty function and expected discounted dividend function.In order to visually explain the analytical conclusions of this article,at the end of this article,based on the Matlab software,the numerical examples of the compound Poisson risk model under the mixed dividend strategy with constant interest rate are given,the intuitive numerical graphs of Gerber-Shiu's expected discounted penalty function under different parameter settings are given,and the effects of changes in the corresponding parameters(threshold,interest rate,and periodic dividend time point distribution distribution)on the corresponding performance function values are analyzed and explained.This paper analyzes the Gerber-Shiu expected discounted penalty function and expected discounted dividend function of the compound Poisson risk model under the mixed dividend strategy under the influence of interest rates,the research object of this model more realistically measures the operating risk of insurance companies.At the same time,the conclusion of this article provides theoretical guidance for the insurance company's capital management,and has guiding significance for the stable operation of insurance companies.