The Barrier Strategy Of Two Kinds Of Risk Models At Random Observation Times

The dividends problem is one of the most important problems in Finance and In-surance research.In this paper-we mainly use the theory and method of probability and statistics to study the dividends of two kinds of risk models.One type is Ornstein-Uhlenback type model,the other type is Markov-modulated dual risk model.This paper consists of three primary parts.The first chapter is the introduction,which introduces the Ornstein-Uhlenback type model and the Markov-modulated dual risk model.More over,we introduce the research status of strategy dividends in risk model,and introduces the barrier strategy dividends at random observation times in this paper.The second part,we consider a barrier strategy dividends and its optimal dividends at random observation times in a type of Ornstein-Uhlenback type modle.Firstly,we use double expectation formula to derive integral-differential equations of the expected dis-counted dividends of this model until ruin time.Secondly,we obtain differential equations of the expected discounted dividends until bankruptcy under a barrier strategy.Then in term of the different initial surplus of companies,we derive explicit expression of the expected discounted dividends.Subsequently,the optimal barrier is determined.In the third part,we consider a barrier strategy dividends at random observation times in a type of Markov-modulated dual risk model.And we use double expectation for-mula to derive integral-differential equations of the expected discounted dividendy until ruin time according to three factors of occurrence of income arrival process?occurrence of dividends and the change of environment state.Further more,we derive the solution of the expected discounted dividends in two state case when the income distribution is exponential.