Analysis Of The Risk Models With Proportional Reinsurance And Linear Dividend Policy

For the classical risk model and various generalized risk model, changeablecharacteristics of the ruin probability are the theoretical basis for the insurancecompany, but we find absolute ruin probability is of great significance in reality. Inaddition, the dividends strategies in insurance risk model, as one of the hot spots inthe current research, has also got more and more attention. Based on the research ofthe reinsurance strategy, dividends strategy, expected discounted penalty functionand absolute ruin probability, the structure of this essay is arranged as follows.Firstly, we introduce the concept, development course, the main developmentdirection and research methods of risk theory at present, and summarize the relevantproperties of the basic risk model thorough the definition and properties of theexpected discounted penalty function in this paper.Secondly, as one core of this thesis, based on the classical risk model, we take inthe proportion reinsurance then establish the Proportional reinsurance risk modelwith interference. By combining the update theorem with the classical risk the-ory, the statistical properties involved the surplus process are simply analyzed andderived. The specific expression of the ruin probability and the adjustment coe?-cient are given when the amount of claims obey the Exponential distribution.Themethod of Solving the ruin probability is di?erent from the traditional method, andwe obtain the ruin probability corresponding risk model through survival probabilityin this article. After that, some numerical examples are presented to show that theoptimal reinsurance strategies to maximize the adjustment coe?cient and minimizesthe ruin probability, while we find these two criteria are equivalent.Finally, as another core of this paper, by considering loans and investment, weestablish the absolute risk model with the linear dividends strategy and interference.The model process is a Markov process, using the Markov property and the totalprobability formula, we give a discount of the integral - di?erential equation onthe Gerber-Shiu function; Then according to specific meanings of the Gerber-Shiufunction under certain conditions, The absolute ruin probability and the Laplacetransform of the absolute ruin time are given when the amount of claims obey theExponential distribution.