Research On Problems Related To The Compound Binomial Risk Model With A Constant Interest

Risk theory is a hot study topic in the realm of modern actuarial science and mathematics, and ruin theory is the core of risk theory. The study of the risk theory started from the PhD paper of Filip Lundberg, who was a Swedish actuarial scientist, in 1903, he first brought up an important stochastic process, Poisson process, in his paper. Cramér developed Lundberg'work based on the mathematics, and formed the base theory of the classical risk theory. At present, the classical risk model has been deeply researched and many important theories have been educed, which have established a stable foundation for the further development of the risk theory. As the theory has many defects, many studiers have been improving it.Based on the works of predecessors, as the continuous time can't be carried out in the actual computational application and the investment policy of the practical society was considered, the compound binomial risk model with a constant interest force was studied in this paper. At first, the generalized form of the classic risk model, the exact expression of the compound binomial model with a constant interest force and the related hypothesis were given out. The related processes were also studied, the Markovian property of the compound binomial model with constant interest force was proved and the transition probability was given out. According to the transition probability, the expansion form of the discounted probabilities was given out. At last the ruin probability was studied, an estimation of the upper boundary of the ruin probability was given out by using the recursive method.