Ruin probability in the continuous-time compound binomial model

The continuous-time compound binomial model, introduced in this paper, is a continuous-time version of the compound binomial model in discrete time. Its skeleton chain is coincided with the compound binomial model and its limiting case is the compound Poisson model. We set the risk model in the framework of PDMP and get a exponential martingale by virtue of the extended generator (coupled with a discrete part) of the PDMP. The theory of change of measures is developed for this model. Some results are derived for the ruin probabilities, such as the general expressions for ruin probabilities, Lundberg bounds and Cramér–Lundberg approximations and etc. All the results are parallel to the corresponding ones in the compound Poisson risk model. And a closed-form expression for the ruin probability is obtained under some special cases.