On The Terminal Time Of Semi-dynamic System And A Class Of Risk Model

In this paper, we concern about the distribution of the terminal time of semi-dynamic system and the ruin probability of a class of risk model.The terminal tune of semi-dynamic system is the generalization of that of stochastic process.In a sense,it can be seen as the time when semi-dynamic system is killed ,or as the time the first random jump of piecewise deterministic Markov process .We go into the distribution of the terminal time of semi-dynamic system and some qualities of its hazard function. It is avail to the research of the terminal tune of piecewise deterministic Markov process .In the second part ,we construct a more general risk model ,that is , the risk model with premium and claim arrial rate depending on the current reserve .We combine this model with PDMP. Clearly,the ruin time is the terminal time of piecewise deterministic Markov process. To this kind of model .with the use of martingale approach, we get the expression of ruinprobabilityThis model is not only thegeneralization of classical risk model, but it include a very interesting case , that is ,the premium and claim arrival rate are depended on the current reserve , but their proportion is constant.In this case , the ruin probability is the same as that of classical risk model on the condition of the same proportion.