Discounted probability of exponential parisian ruin: Diffusion approximation

We analyze the discounted probability of exponential Parisian ruin for the so-called scaled classical Cramér–Lundberg risk model. As in Cohen and Young (2020), we use the comparison method from differential equations to prove that the discounted probability of exponential Parisian ruin for the scaled classical risk model converges to the corresponding discounted probability for its diffusion approximation, and we derive the rate of convergence.