Asymptotic behaviors for a doubly stochastic risk model with delayed claims

In this paper, we study a risk model with delayed claims in which main claims exceeding a preset threshold trigger by-claims. Claim arrivals follow a doubly stochastic Poisson process. By constructing an exponential martingale, large and moderate deviation principles for the aggregate loss process are established. Furthermore, we derive exponential bounds and asymptotic estimates for the ruin probability. Simulation study results validate the accuracy of our theoretical asymptotic behaviors.