# A note on Parisian ruin under a hybrid observation scheme

## TL;DR

This paper investigates Parisian ruin probabilities under a hybrid observation scheme combining Poisson and continuous monitoring, providing improved fluctuation identities expressed via second-generation scale functions.

## Contribution

It extends previous models by deriving new fluctuation identities for Parisian ruin under hybrid observation, enhancing analytical tools for risk process analysis.

## Key findings

- Derived improved fluctuation identities for Parisian ruin.
- Expressed identities using second-generation scale functions.
- Enhanced understanding of hybrid observation schemes in risk models.

## Abstract

In this paper, we study the concept of Parisian ruin under the hybrid observation scheme model introduced by Li et al. \cite{binetal2016}. 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 \cite{binetal2016} and we compute other fluctuation identities. All identities are given in terms of second-generation scale functions.