The Results Of Bankruptcy For Two Classes Of Risk Model With Paying Dividends

Studies of the risk theory were originated from the Sweden actuary Lundberg one hundred years ago. With the development of financial market and the change of the business environment of insurance company, the classical risk model can’t describe the real risk profile to a large extent. Dividend strategies for insurance risk models were firstly proposed by De Finetti in a paper presented to the International Congress of Actuaries in New York in 1957. Obviously, the theories about dividend strategies are very valuable in the devising and managing of products with dividends. The model with paying dividends has become a hot issue in the field of the modern actuarial science and mathematics. Correspond to the modern insurance company’s actual need, many research in modern actuarial theory are focused on the random environment. The study of the risk model with varying premiums rate which fits the fact more precisely is also arising. Considering the variable premium rate, the premium rate is generally regarded as the function of surplus. Besides the premium rate, risk models with interest also have been studied by many researchers.In this paper, we firstly study the expected discounted penalty function, the moments of surplus before ruin and deficit at ruin, and the Laplace transform of ruin time in the continuous-time compound binomial risk model with paying dividends; then we consider the compound Pascal model with paying dividends and variable premium under stochastic interest rates, we study the ruin probability and the joint distributions of this model.