离散模型下最优红利再保策略
发布时间：2018-11-19 09:41
【摘要】：随着保险市场的不断开放与发展,保险业的竞争越来越激烈,保险企业需要不断开发更具竞争性的产品,以及通过购买再保险等方法来增加保险公司自身的盈余水平与抗风险能力.而作为衡量保险公司盈利水平的红利优化问题的研究对于保险公司的管理决策有着重大的意义.因此,该类问题已经成为当今保险业新的研究热点. 本文主要针对经典复合二项模型来研究离散模型下的最优红利再保策略.即我们研究的是保险公司在收取一定的保费并做出索赔后所作的分红和再保险决策.该决策是带固定上界且取整数值并与当前瞬时盈余有关的的一类支出函数,该支出函数包含可能购买再保险的再保费以及支付给股东的红利,优化目标是使该决策的值函数达到最大.我们围绕该支出函数考虑购买超额损失再保险和考虑资本重置的再保险,最终我们发现值函数是一类离散HJB方程的唯一解,从而我们得到最优的支出策略、红利策略和对应的最优再保险. 本文第一部分考虑超额损失再保险,得到一个双控制对象的优化问题.我们采用两步优化的方法来解决该问题,即先只考虑总体支出(不购买再保险时的情况,仅考虑单控制对象),得到最优的支出(红利)策略,再利用值函数的一个变换得到了最优值函数和最优红利策略的一种较简单的计算方法;然后在总体支出固定的基础上考虑可能购买超额损失再保险的最优再保策略,我们得到了最优的免赔额. 在第二部分,我们考虑的是一种新型的再保险.这种再保险是由股东从红利中拿出一定的比例来支付再保费,由再保险公司提供随机资本注入的资本重置再保险.我们得到了最优的支出策略、红利策略与最优的再保费比例. 相应的数值解能够很好的验证我们的理论.另外,分析对应的数值结果,我们还发现资本重置再保险时的值函数优于购买超额损失再保险时的值函数.
[Abstract]:With the continuous opening and development of the insurance market, the competition of the insurance industry is becoming more and more intense. Insurance enterprises need to develop more competitive products. And through the purchase of reinsurance and other methods to increase the level of surplus and risk-resistant insurance companies. As a measure of the profit level of insurance companies, the study of dividend optimization is of great significance to the management decisions of insurance companies. Therefore, this kind of problem has become a new research hotspot of insurance industry. In this paper, the optimal dividend reinsurance strategy under discrete model is studied for classical compound binomial model. That is to say, we study the dividend and reinsurance decision made by the insurance company after collecting a certain premium and making a claim. The decision is a class of expenditure functions with fixed upper bounds and rounding values related to the current instantaneous surplus, which includes reinsurance premiums that may be purchased and dividends paid to shareholders. The objective of optimization is to maximize the value function of the decision. We consider buying excess loss reinsurance and capital replacement reinsurance around the expenditure function. Finally, we find that the value function is the unique solution of a class of discrete HJB equations, and we obtain the optimal expenditure strategy. Bonus strategy and corresponding optimal reinsurance. In the first part of this paper, we consider the reinsurance of excess loss and obtain an optimization problem of double control object. We use a two-step optimization method to solve the problem, that is, we only consider the overall expenditure (not the case of reinsurance, only consider the single control object), and get the optimal expenditure (dividend) strategy. A simple method for calculating the optimal value function and the optimal dividend strategy is obtained by a transformation of the value function. Then we consider the optimal reinsurance strategy which may buy excess loss reinsurance on the basis of the fixed total expenditure, and we obtain the optimal deductible amount. In the second part, we consider a new type of reinsurance. This reinsurance is paid by shareholders in a certain proportion from the dividend, and the reinsurer provides the capital replacement reinsurance with random capital injection by the reinsurance company. We obtain the optimal expenditure strategy, dividend strategy and optimal reinsurance ratio. The corresponding numerical solutions can well verify our theory. In addition, by analyzing the corresponding numerical results, we find that the value function of capital replacement reinsurance is better than that of excess loss reinsurance.
【学位授予单位】：湘潭大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F840.3;F224;O225
本文编号：2341901
[Abstract]:With the continuous opening and development of the insurance market, the competition of the insurance industry is becoming more and more intense. Insurance enterprises need to develop more competitive products. And through the purchase of reinsurance and other methods to increase the level of surplus and risk-resistant insurance companies. As a measure of the profit level of insurance companies, the study of dividend optimization is of great significance to the management decisions of insurance companies. Therefore, this kind of problem has become a new research hotspot of insurance industry. In this paper, the optimal dividend reinsurance strategy under discrete model is studied for classical compound binomial model. That is to say, we study the dividend and reinsurance decision made by the insurance company after collecting a certain premium and making a claim. The decision is a class of expenditure functions with fixed upper bounds and rounding values related to the current instantaneous surplus, which includes reinsurance premiums that may be purchased and dividends paid to shareholders. The objective of optimization is to maximize the value function of the decision. We consider buying excess loss reinsurance and capital replacement reinsurance around the expenditure function. Finally, we find that the value function is the unique solution of a class of discrete HJB equations, and we obtain the optimal expenditure strategy. Bonus strategy and corresponding optimal reinsurance. In the first part of this paper, we consider the reinsurance of excess loss and obtain an optimization problem of double control object. We use a two-step optimization method to solve the problem, that is, we only consider the overall expenditure (not the case of reinsurance, only consider the single control object), and get the optimal expenditure (dividend) strategy. A simple method for calculating the optimal value function and the optimal dividend strategy is obtained by a transformation of the value function. Then we consider the optimal reinsurance strategy which may buy excess loss reinsurance on the basis of the fixed total expenditure, and we obtain the optimal deductible amount. In the second part, we consider a new type of reinsurance. This reinsurance is paid by shareholders in a certain proportion from the dividend, and the reinsurer provides the capital replacement reinsurance with random capital injection by the reinsurance company. We obtain the optimal expenditure strategy, dividend strategy and optimal reinsurance ratio. The corresponding numerical solutions can well verify our theory. In addition, by analyzing the corresponding numerical results, we find that the value function of capital replacement reinsurance is better than that of excess loss reinsurance.
【学位授予单位】：湘潭大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F840.3;F224;O225
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