Research On The Parisian Ruin Under The Classical Risk Model With Two-Step Premium

In risk theory,the study of ruin probability and ruin time has always been an important topic.In the classical risk model,when an insurance company’s surplus reaches negative value,ruin is declared.With the vigorous development of the financial insurance theory,the definition of classical bankruptcy cannot meet the requirements of the development of the times,and the concept of the Parisian ruin is born.The Parisian ruin refers to the declaration of bankruptcy after the insurance company’s surplus reaches negative value for a period of time,which provides a window period for the insurance company to solve the deficit crisis and sort out the finances to resume normal operations.It is a more reasonable risk measure than the classical ruin.In view of this,this paper mainly studies the Parisian ruin under the classical risk model with two-step premium.The first chapter mainly introduces the relevant knowledge of Parisian ruin,the classical risk model with two-step premium and its nature.And research results of Parisian ruin under deterministic delay and random delay.Secondly,the research background of the Parisian ruin and related issues and the current research status are introduced.Finally,the organization of each chapter of the paper and its innovation points are described.The second chapter mainly studies the probability of Parisian ruin probability under the classical risk model with two-step premium.Firstly,by using the strong Markov property of the model and the theory of hitting time,the expression of the probability of Parisian ruin is derived.Secondly,an exact expression of the probability of Parisian ruin is obtained for the exponential claims.Finally,numerical examples are given to illustrate the relationship between the Parisian ruin probability and the delay,and the comparison between the Parisian ruin probability and the classical ruin probability under the different initial assets,the claims strength and the premium is given.The third chapter mainly studies the Laplace transform expression of Parisian ruin under the classical risk model with two-step premium.Firstly,the Laplace transform expression of the time of the Parisian ruin is obtained by using the strong Markov property of the model and using the Excursion theory.Secondly,under the exponential claims,the exact expression at the Laplace transform of the time of the Parisian ruin is obtained.Finally,numerical examples are given to study the effect of the changes in the claims strength,delay and the premium rate on the Laplace transform of the time of the Parisian ruin.