The Parisian Bankruptcy Problem Of Refraction Lévy Risk Process With Mixed Observation Strategy

In this paper,we use a temporal approach to study Parisian ruin for a Lévy process with an adaptive premium rate,namely a refracted Lévy risk process.Our method is based on a hybrid observation scheme switching between discrete and continuous observations,which can be called a temporal approach as opposed to the spatial approximation approach.The hybrid observation scheme involved here combines discrete observation(Poisson observation)and Parisian delay.More specifically,we discretely in the "non-interested" zone(when surplus is positive)and continuously in the "interested" zone(when surplus is negative).It is another extension of the classical ruin such that the event of ruin is monitored discretely at independent Poisson arrival times.This paper generalizes the models studied by Li et al.(2018).And we generalized the risk processes from a spectrally negative Lévy risk process to a refracted Lévy risk process with a refractive level of b=0.The Parisian ruin probability of this model is also discussed,and the scale functions are used to give an expression of Parisian ruin probability.Finally,two examples are given to calculate the Parisian ruin probability for the special refracted Lévy risk process.The paper is organized as follows.Chapter 1 is a introduction.In this part,we mainly introduces the concept of Parisian ruin,refracted Lévy process and Parisian ruin time.In the second chapter,spectrally neg-ative Lévy process,scale function and fluctuation identities are introduced;Refracted Lévy risk processes are given in the second part;in the last part,we give some fundamental lemmas.The hybrid observation scheme is given in the third chapter.In Chapter 4,we presented and proved the main theorem and lemmas.Two examples are given in the fifth chapter.At the last chapter,we give a summary and prospect of the article.