Several Types Of Discrete Risk Model, Ruin Probability

Regarding the classic discrete time risk models, they discussed thecompletely discrete compound binomial model. In these models, thelistribution of the individual claims is also discrete. Regarding the generalcompound binomial models, the discussion is very little. Also a single insurerof the classic separate risk model cannot satisfy the insurance companyrequirements.Therefore, we first create the two-binomial risk model. In this model, itspremiums collecting process and claims process are also compound binomialprocess. Following, we create a two-type discrete time risk model .In thismodel, its premiums collecting process is Poisson sequence, the arrival of onetype claims is a Poisson sequence, and the arrival of the other type claims is abinomial sequence. Finally, considering the interest rates, investment incomeand the random risk as a combination factor, we establish a two-type ofdisturbance discrete risk model.On the model, we use the analysis of martingale, and obtained theultimate ruin probability and Lundberg inequality.