With A Constant Dividend Boundary Strategy Dependent Erlang Risk Model

This dissertation is devoted to dealing with the Gerber-Shiu expected dis-counted penalty function and the expected discounted dividend function on theErlang risk model with dependence under a dividend strategy. The dividendstrategy is the constant barrier dividend strategy and the dependence is a specialcase of dependence which can describe the earthquake insurance.In actuarial science of insurance, the independence is a powerful property,which simplifies mathematical operations and smoothes away most ruin problems.But in the actual operations of the insurance company, the independence tendto be untenable. For example, in the earthquake insurance, claim size is oftenafected by inter-claim time. Therefore, the researchers begin to take dependenceinto the risk model. On the other hand, with the stock market in full swing, manyresearchers focus on the dividend of the insurance company. They put forwardseveral dividend strategies and start to study the risk model under a dividendstrategy. The research to the risk model with dependence under a dividendstrategy has momentous current significance.According to the contents, this dissertation is divided into three chapters:Chapter1is the introduction. It briefly introduces the historical backgroundand research situation of ruin theory. Then, it gives the main contents of thisdissertation.Chapter2studies the Erlang(2) risk model with dependence under constantbarrier dividend strategy. Section1is the preliminary knowledge, which givesthe definition of the risk model and the research of the pioneers. In Section2,we improve the method to study the Gerber-Shiu expected discounted penaltyfunction of this model. When u≤b, we first derive the integral equation forthe Gerber-Shiu expected discounted penalty function. Then, we use operatorsrepeatedly to get the integro-diferential equation. Finally, we take this to becompared with the known results. In Section3, we study the expected discounteddividend function of this model.When u≤b, we first derive the integral equationfor the expected discounted dividend function. Then, we use operators repeatedlyto get the integro-diferential equation. Finally, we take this to be compared withthe known results. Chapter3studies the Erlang(n) risk model with dependence under constantbarrier dividend strategy. Section1is the preliminary knowledge, which gives thedefinition of the risk model. In Section2, we discuss the Gerber-Shiu expecteddiscounted penalty function of this model. When u≤b, we first derive the inte-gral equation for the Gerber-Shiu expected discounted penalty function. Then,we use operators repeatedly to get the integro-diferential equation. Finally, wetake this to be compared with the corresponding conclusions in Chapter2. In Sec-tion3, we study the expected discounted dividend function of this model. Whenu≤b, we first derive the integral equation for the expected discounted dividendfunction. Then, we use operators repeatedly to get the integro-diferential equa-tion. Finally, we take this to be compared with the corresponding conclusions inChapter2.