The Research On Dividend Strategy With Investment In The Risk Model

In this paper,we study a dividend strategy with investment in the risk model.In the process of company management,there is a very important issue is to give shareholders a dividend.The amount of dividends and the time of dividends are issues to be studied in Actuarial Science.If the amount of the dividends is too large, or the time to distribute dividends is not appropriate,will make the company operation is affected or even suffer a loss.If the amount of the dividend is too small, it will harm the interests of shareholders.How to seek a criterion to balance the interests of shareholders and the company is the key to the research. There are four main research methods of dividend strategy, many scholars have done the different angles of research for these dividend strategy and they obtained some good results.In the classical risk model,the time of surplus U(t) is firstly less than 0 is the time of business failure. That is for the risk process U(t),the ruin time is ? = inf{t|U(t) < 0},ruin probability?(u) = P(? < ?|U(0) = u).This kind of ruin is relatively bankruptcy.In the past, the research on the issue of ruin is based on this.However, in real life, we know that the bankruptcy of the company is usually not at the time ?. In order to make the conclusion more close to the reality, this article will be different from the classical risk model of bankruptcy. We introduce a function ?(x) to describe the relationship between negative surplus and failure probability to do the research of related problems.In 1968, Mossion studied the Multi-period investment, but he didn't obtain its analytical expression.After that, many scholars have carried out relevant research. In [20], Hakansson did further research of it. In [23], Dumas and Luciano studied the dynamic portfolio selection under transaction cost. In[24] Schweizer studied the optimal hedge variance. There are a lot of scholars have studied the related questions of multi-stage investment, but no analytical solutions were obtained. Later in the article [7],using the method of embedding, the analytic expression of multi stage dynamic investment was studied under the condition of self financing. In practice, investors tend to increase or decrease the amount of money based on the market or their own situation.Based on the above research background, my master's thesis mainly did the following research: First of all, the multi stage investment strategy with dynamic capital injection was studied, and the analytical formula is obtained under the maximization of the utility function.Secondiy, verified the effectiveness and scientific of the investment strategy. Using Matlab to do the optimal simulation research, obtained optimal investment strategies under different utility function. Thirdly, studied a dividend strategy with investment in the Omega model.The dividend strategy consists of two types of dividend. If at a potential dividend-payment time the surplus is above k, part of the excess are paid as dividends directly, the other part are used as dynamic investment capital, at a particular time, the sum of profits and investment capital will be paid as another dividend.