Dividend Distribution And Capital Injection In The Dual Model Of Constant Interest Rate

Actllarial science has made great progress in rcent years.However,people gracdual-ly found that there are many problems that cannot be solved simply bv the traditional Cramer-Lundberg risk model,so the dual model came into being.The dual model plays an irreplaceable role in the dylamic dcpiction of some companyis'surpluses,such as mineral resource development companies similar to petroleum companies and inventive companies similar to pharmaceutical companies.In actuarial science,the issue of dividends has always been a hot issue in the field of actuarial science.Many scholars have proposed and improved a variety of dividend strategies.In order to enable the company to operate for a long time and enable shareholders to obtain more benefits,people start research to inject certain money into the conmpany when neeessary to enable the copmany to survive a short-term bankruptcy crisis.Because the funds have time attributes,people find that in a.ddition to dividends or capital injections will affect the company's earnings,interest rates in daily life will continue to change the company's earnings.This paper mainly considers the optimal periodic dividend prolblem in the dual model with constant interest,capital injections and transaction fees.Taking the fixed constant interest rate as the influencing factor of the surplus into the dual model,the dividond is distributed according to the periodic dividend strategy,and the company is injected with funds at the necessary time.In addition,due to the cost of capital flow,this article combines the actual situation,when distributing dividends to shareholders,it is necessary to deduct the dividend transaction fee according to a certain proportion.When injecting capital into the company,not only need to spend a certain percentage of the costlbut also each fixed Capital injection fees,these arc also important factors affecting the company's earnings and dividends.According to the content,this paper is divided into the following five chapters:the first chapter is the introduction,which mainly introduces the dual model with constant interest rate,the background and research status of dividend and capital injection.The second chapter is the basic knowledge,mainly introduces the concrete form of the dual model with constant interest rate and the symbolic representation of dividend and capital injection,and gives the definition of the target value function.In the third chapter,the optimal periodic dividend strategy is studied by using the dynamic programming principle without considering the capital injection,and the equa-tion of the dividend value function under the optimal policy and the dividend threshold corresponding to the optimal policy is solved.In the fourth chapter,the influence of capital injection on dividend is considered,and the optimal periodic dividend and capital injection strategy are studied by using the dynamic programming principle,and the equation of the dividend value function under the optimal strategy and the dividend threshold corresponding to the optimal strategy is solved.The fifth chapter comprehensively analyzes the optimal strategy in the case of capital injection and no capital injection.The sixth chapter summarizes the results and shortcomings of this paper and the di-rection that can be worked on in the future.