Study On Upper Bounds For Ruin Probability And Some Results Of Constant Dividend Barrier Of Risk Model

The ruin model which describes the risk of insurance company from the dynamic perspective is very important in risk theory. It is used as a measure of the risk of the portfolio and a risk index for reinsurance. Nowadays, dividend product of insurance becomes a important new type product. So the research of dividend barrier becomes very practicality for making decision.In the first section, we will give some concepts of the ruin theory, and introduce the well-know Lundberg equality, namely the exponential upper bounder. In succession, we introduce some basic tools for our research, such as martingale, stopping time, Markov chain, and so on.Risk models with interest are widely studied in practice. In the second section, we consider generalized discrete time risk processes with a Markov chain interest model proposed by Jun Cai. Martingale inequalities are used to obtain non-exponential upper bounder for the ruin probability. Two numerical examples are given to illustrate these results.In the third section, we derive some results on the dividend payments prior to ruin in the classical risk process with interest. Integro-differential equation with boundary condition satisfied by the expected present value of dividend payments is derived and solved. Further we derive integro-differential equation for the moment generating function, through which we analyze the higher moments of the present value of dividend payments. Finally, closed-form expressions for exponential claims are given.