Threshold Dividend Research Under A Capital-Exchange Agreement

In the modern society of competition incentive,enterprises have to select the best and eliminate the worst in competition.In order to have a place in the market,enterprises not only need careful management,but also need to cooperate with each other.In terms of company operation,capital turnover and capital chain observation,as asset accounting and dividend usually occur at discrete time points,it is difficult to make effective observation on assets in continuous time.Therefore,based on the capital-exchange agreement model studied by Albercher,this paper introduces random observation and utilizes the randomness of discrete time points to realize effective observation of the company’s earnings,promote better and faster development between companies,and further make the model more reasonable.This paper mainly studies the expected cumulative discounted dividends of the capital-exchange agreement model with random observation under the threshold dividend strategy.The sine approximation method is used to calculate the expected cumulative discounted dividends.The main content of this paper is as follows:The first chapter briefly discusses the background of risk theory,the latest research trends and the main content of this paper.The second chapter introduces the preliminary knowledge of sine function approximation and the risk model involved in this paper.In chapter 3,we discuss the expected discounted dividends of two companies under the capital-exchange agreement protocol model with random observation,and obtain the integro-partial differential equation and the corresponding boundary conditions of the expected discounted dividends when the time interval of random observation obeys the exponential distribution.Due to the complexity of the equation,it is impossible to calculate its display solution.In this paper,the sine approximation method is adopted to obtain the numerical solution of the expected discounted dividends.