We study moderate deviations for maximum likelihood estimators of parameters in generalized squared radial Ornstein-Uhlenbeck processes. The moderate deviation principles of the two parameters are established.

Applying the large deviations and moderate deviations for the log-likelihood ratio of the Jacobi model, we give negative regions in testing Jacobi model, and get the decay rates of the error probabilities.

Sample path large and moderate deviation principles for Markov modulated risk models with delayed claims are proved by the exponential martingale method. As applications, asymptotic estimates and exponential bounds of the ruin probability are also studied.

In this paper, we obtain a moderate deviation result for the maximum likelihood estimator under certain regular conditions. Two examples of non-regular cases are studied.