In this paper, we study the asymptotic behavior of randomly perturbed Chan–Karolyi–Longstaff–Sanders (CKLS) model with small parameter ε. When ε→0, the central limit theorem and moderate deviation principle for the solution of randomly perturbed CKLS model are obtained.

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.

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.

We obtain the rate of convergence of the functional limit for increments of a d-dimensional Brownian motion. As an application of the main result, we get a d-dimensional version of the result on the size of small increments of a Brownian motion.

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.

In this article, we consider the problem of the minimal entropy martingale measure of a jump process influenced by jump times. The minimal entropy martingale measure of the price process is given out by the exponential martingale method, and the expression of the corresponding relative entropy...