The Optimal Dividend-reinsurance Strategy In Discrete Model

With the increasing opening-up and development of insurance market, theinsurance industry increasingly competitive.Insurance companies need to developmore competitive products constantly, and through the method of the reinsuranceto improve the level of the insurance company’s surplus and the ability to resistrisks. And the research of the dividend optimization problems is a standard tomeasure the proft level of the insurance company, which has great signifcancefor the management and decisions of the insurance company. Therefore, this kindof problem has become the new research hotspot in today’s insurance.In this paper, we used the classical compound binomial model to investi-gate the optimal dividend reinsurance strategies in discrete risk model.That isto say, we study the decisions of the insurance companies after the insurancecompanies charge a premium and to make a claim, which enable the insurers tomore efcient working capital and better control risk.The decision is a class ofexpenditure function with constant boundary which take an integer value anddepend on the current instantaneous surplus.in the paper,the expenditure func-tion contains the reinsurance premium that the reinsurance may be purchasedand dividends that paid to shareholders. The goal of the decision is to maximizethe dividends of value function.We take into account purchase the excess of lossreinsurance and resetting capital reinsurance arounding the expenditure function,eventually we found that the value function is the unique solution of a discreteHamilton-Jacobi-Bellman equation, and resulting in the optimal expenditure pol-icy, dividend policy and the corresponding optimal reinsurance.In the frst part of the paper, we consider the excess of loss reinsuranceand can get the problem of the double control object optimization.we used themethod of substep optimization to consider the overall paying out (the situationof not purchase insurance, only consider single control object)and get optimalexpenditures (dividend) policies.at frst; and then we used a transformationof value function to get the a simple calculation method of the optimal value function and optimal dividend policy.After this, on the basis of the fxed overallexpenditure,considering perchase optimal reinsurance policy, we also get theoptimal deductible amount.In the second of the paper, we consider a new type of reinsurance that thestockholders take a certain proportion from the dividend to buy reinsurance pre-mium, and the resetting capital reinsurance of the random capital injection whichprovide by the reinsurance companies. And we can get the optimal proportion ofexpenditure policy, dividend policy and the optimal ratio.The corresponding numerical solution can be very good to verify our theo-ry.In addition, analysis the corresponding numerical results, we can fnd that thevalue function of the resetting capital reinsurance better than the value functionof the excess of loss reinsurance.