A note on Parisian ruin under a hybrid observation scheme

In this paper, we study the concept of Parisian ruin under the hybrid observation scheme model introduced by Li et al. (2018). Under this model, the process is observed at Poisson arrival times whenever the business is financially healthy and it is continuously observed when it goes below 0. The Parisian ruin is then declared when the process stays below zero for a consecutive period of time greater than a fixed delay. We improve the result originally obtained in Li et al. (2018) and we compute other fluctuation identities. All identities are given in terms of second-generation scale functions.