ABSTRACT
Dividends problem was first proposed by De Finetti at the 15th International Congress of Actuaries in 1957, then it became a hot issue that was discussed by many scholars. With the development of dividend strategy, people begin considering such a problem as the shareholders get the dividend profit, whether they should be obliged to help the company when it encounters diculties. Dickson&Waters (2004) pointed that the shareholders should cover the deficit at ruin, that is, inject capital. So the surplus at the time of ruin is then 0 and the company survives. Capital injection strategy provides an approach to keep the company running smoothly. Gerber et al. (2006), Kulenko&Schm idli (2008), and He&Liang (2009) had discussed such a strategy. The literature[1] discussed that the optimal dividend of the classical risk model is band dividend strategy, When the company deficit occurs, it allows shareholders to invest. The literature[2] derived the optimal dividend and capital injection strategy of the compound Poisson model with interference. Based on the previous studies, this article discussed dividends problem of the classical risk model with minimum surplus and fixed transaction costs constraints.
