Abstract:

The author provided the exact forms of moderate deviation for the Poisson ARCH(1) process. In addition, the author used Poisson ARCH(1) process to model the claim frequency in the risk model. With the help of moderate deviation result, the author derived the uniform asymptotic formula for the finitetime ruin probability.

Key words: Poisson ARCH(1) process, moderate deviation principle, finitetime ruin probability