The Dividend Strategies In The Compound Binomial Risk Model

In this paper, we consider two questions.First, we consider the compound binomial model modified by the inclusion of stochastic return on the investments by an insurer, and adding a dividend policy to the classical risk model. The dividend policy is that when the surplus is bigger than a positive integer b, the insurer pays out all of the surplus over b as dividends. In Section 2.3 we find that the expected value of the first dividend (the dividend paid at the first hitting time of (b,∞) for the surplus process) before ruin satisfies a set of linear equations, and obtain its solution. Similarly, we find some results about all dividends (the accumulated dividends) up to the ruin time. In Section 2.4 we will derive the distribution of the first dividend paid before ruin. And in Section 2.5 we will get the distribution of the number of the dividend payments, and the distribution of the accumulated dividends before ruin.For the second question in the present paper, we consider the compound bi-nomial risk model with a constant interest rate, a constant dividend barrier and periodic dividend payments, etc. In this model, dividends are paid only probably at some given times that occur periodically. In my opinion, this way for the dividend payments is closer to practice than that in the models mentioned in references in the end of this paper. In addition, the dividend strategy in the present paper is so flexible that can become a barrier strategy or a band strategy, etc. because the dividends are paid according to not only a dividend barrier but also an undeter-mined function of the surplus which can be devised according,to the need of the insurer, see Section 3.2. In this paper, the analysis is mainly focused on the eval-uation of the expected present value of dividend payments until ruin, organized in Section 3.3. The arbitrary moments of discounted dividend payments is discussed in Section 3.4.