Some Study On The Impulsive Dividend

In recent years,dividends gradually become a hot research topic in the risk theory,such as barrier dividends,threshold dividends and impulsive dividends,especially the study of impulsive dividends are more and more in-depth.But the current research of impulsive dividends is based on the classical risk model,so it is necessary to extend it to the dual risk model,and the dual risk model has great application in reality,such as oil companies,oil is consumed every year,and new oil fields are detected suddenly.In addition,in reality,the claim amounts and the claim interval are often not independent,so it is necessary to study the impulsive dividends under the dependent model.This article is divided into the following five chapters:In chapter one,this paper reviews the origin and development of insurance,the current situation of risk theory,and introduces the research background and main work of this paper.In chapter two,a brief introduction is given to the classical risk models,im-pulsive dividends,dual risk models and Farlie-Gumbel-Morgenstern-copula(FGM-copula)dependency.In chapter three,we study the impulsive dividend under the dual model,obtain an integral differential equation for Gerber-Shiu function,and the integral differential equation is analyzed when the claim is exponential distribution.Then we studied the number of dividends before ruin,and discounted expectation of total amount of dividends before ruin.In chapter four,we think about the impulsive dividend under the FGM-copula dependent model,and study the Gerber-Shiu function under the model.In chapter five,we summarize the paper and prospects the possible research directions.