费率受制于位相半马氏过程的风险模型

Risk Models of the Premium Rates Which is Controlled By Phase Semi-Markov Process

对带马氏链的线性和非线性系统 ,经过众多学者近 2 0多年的努力 ,已取得一系列重要成果。然而 ,由于马氏链状态逗留时间服从负指数分布 ,使得这些成果在应用中有很大的局限性。本文首先探讨了位相半马氏过程的性质 ,然后以位相半马氏过程代替马氏过程 ,研究风险模型的相关问题 ,取得了与马氏链相同的研究成果 ,从而说明了位相半马氏过程在克服由马氏过程带来的局限性中的作用。

Over the past two decades, many efforts are made o n the problems for linear and nonlinear systems with Markov chains, and a number of results are achieved.However, due to the negative exponential distribution o f the time when a Markov chain sojourn at a state, there are many restrictions f or the existing results in practical applications. This paper studies the relate d problems to risk models, uses the phase type semi-Markov processes to replace the finite Markov processes, same results are obtained. A phase semi-Markov pr ocess is successful to overcome the restriction of Markov process.