Limit theorems for non-Markovian marked dynamic contagion processes

In this paper, we study a general dynamic contagion process that includes several standard point processes as special cases. We have developed (i) the corresponding large deviation principle; (ii) the corresponding law of large numbers; (iii) the corresponding central limit theorem, all of which are critical in describing the essential of this type of processes, and are not available in current literature. The proposed model provides a broader framework in the study of contagion processes in various applications. In particular, we obtain the finite-horizon and infinite-horizon ruin probability asymptotics for the risk model with marked dynamic contagion claim arrivals as an application.