Study On Some Problems In Dual Risk Models With Barrier Dividend

Risk theory is one important part of actuarial mathematics theory. With thecontinuous development of the discipline of probability theory and the stochasticprocesses in these years, risk theory has gradually been improved and the insuranceindustry has rapidly been developed. For insurance companies, there are two aspectswhich are most important: First, it is the income, that policyholders invest into riskinsurance with amounts of money; Second, it is the claims; in other words, theinsurance company insured the claims to the policyholders. Proceeding from reality,insurance company is in order to get better returns. It is particularly important to studyrisk model with the probability of the sequence of surplus and claims. So, the risk ofbankruptcy probability model is one more important critical object. With thedevelopment of risk models, many people study the dual model and get some results.The dual risk model with dividend strategy has not been developed. This paperinvestigates some problems in the dual model with a constant dividend barrier,considers issues which is related to the dual risk model with wall dividend strategy, andstudies the probability of bankruptcy.This paper is divided into the following chapters:The first chapter is an introduction, which tells the historical background anddevelopment of risk theory, as well as a review of important research results of the riskmodel, such as the classical model of the probability of bankruptcy and the expecteddiscounted penalty function. Then it focuses on the key findings of dual risk theory.The second chapter briefly introduces some important knowledge that is related tothis paper in order to facilitate the understanding of the main content of this paper.In Chapter3, this paper investigates the ruin problem in the dual model with aconstant dividend barrier. The integral and integral-differential equations for expecteddiscounted penalty function until ruin are derived. The probability in ruin with barrierdividend in the dual model is solved when the individual profit size distribution isexponential.In Chapter4, we consider the Erlang(2) risk model with a dividend barrier strategyin the dual model. The integro-differential equation for expected discounted dividendsuntil ruin is derived and solved when the individual profit sizes distribution isexponential. Finally, we get the integro-differential equation of the ruin probability.