離散模型下最優(yōu)紅利再保策略
發(fā)布時間：2018-11-19 09:41
【摘要】：隨著保險市場的不斷開放與發(fā)展,保險業(yè)的競爭越來越激烈,保險企業(yè)需要不斷開發(fā)更具競爭性的產(chǎn)品,以及通過購買再保險等方法來增加保險公司自身的盈余水平與抗風(fēng)險能力.而作為衡量保險公司盈利水平的紅利優(yōu)化問題的研究對于保險公司的管理決策有著重大的意義.因此,該類問題已經(jīng)成為當(dāng)今保險業(yè)新的研究熱點. 本文主要針對經(jīng)典復(fù)合二項模型來研究離散模型下的最優(yōu)紅利再保策略.即我們研究的是保險公司在收取一定的保費并做出索賠后所作的分紅和再保險決策.該決策是帶固定上界且取整數(shù)值并與當(dāng)前瞬時盈余有關(guān)的的一類支出函數(shù),該支出函數(shù)包含可能購買再保險的再保費以及支付給股東的紅利,優(yōu)化目標(biāo)是使該決策的值函數(shù)達到最大.我們圍繞該支出函數(shù)考慮購買超額損失再保險和考慮資本重置的再保險,最終我們發(fā)現(xiàn)值函數(shù)是一類離散HJB方程的唯一解,從而我們得到最優(yōu)的支出策略、紅利策略和對應(yīng)的最優(yōu)再保險. 本文第一部分考慮超額損失再保險,得到一個雙控制對象的優(yōu)化問題.我們采用兩步優(yōu)化的方法來解決該問題,即先只考慮總體支出(不購買再保險時的情況,僅考慮單控制對象),得到最優(yōu)的支出(紅利)策略,再利用值函數(shù)的一個變換得到了最優(yōu)值函數(shù)和最優(yōu)紅利策略的一種較簡單的計算方法;然后在總體支出固定的基礎(chǔ)上考慮可能購買超額損失再保險的最優(yōu)再保策略,我們得到了最優(yōu)的免賠額. 在第二部分,我們考慮的是一種新型的再保險.這種再保險是由股東從紅利中拿出一定的比例來支付再保費,由再保險公司提供隨機資本注入的資本重置再保險.我們得到了最優(yōu)的支出策略、紅利策略與最優(yōu)的再保費比例. 相應(yīng)的數(shù)值解能夠很好的驗證我們的理論.另外,分析對應(yīng)的數(shù)值結(jié)果,我們還發(fā)現(xiàn)資本重置再保險時的值函數(shù)優(yōu)于購買超額損失再保險時的值函數(shù).
[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.
【學(xué)位授予單位】：湘潭大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2013
【分類號】：F840.3;F224;O225
本文編號：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.
【學(xué)位授予單位】：湘潭大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2013
【分類號】：F840.3;F224;O225
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