The Compound Poisson Risk Model With Periodic Capital Injections And Barrier Dividend Strategy

On the basis of the classical risk model,we assume that the surplus level of an insurance company can only be observed at discrete time points,then a new risk model is proposed in this paper by introducing periodic capital injection strategy and barrier dividend strategy into the classical risk model.We denote the set injection line as ^b₁ and the dividend line as ^b₂.At the time of observation,if the surplus level of the insurance company is less than 0,we can declare the insurance company is bankrupt;If the surplus level is between 0 and ^b₁,capital will be injected immediately by shareholders or reinsurers to restore the surplus level to ^b₁;If the surplus level exceeds ^b₂,the excess amount will be paid to shareholders as dividends.This new risk model is of great practical significance since it is much closer to the actual operating model of an insurance company.In this paper,we deduce the explicit expressions of the Gerber-Shiu function by assuming that the inter-observation times are exponential or Erlang?n?distributed,respectively.In addition,we have studied the expected discounted capital injection functions.And we also have done some research about the expected discounted dividend functions.Some relevant numerical examples are presented to help us get more information about the risk model.This essay is organized as follows:In chapter 1,we introduce the significance and the research status at home and abroad of this research;In chapter 2,we present some fundamental conceptions and the risk model studied in this essay;In chapter 3,we study the Gerber-Shiu function,the expected discounted capital injections function and the expected discounted dividend functions when the inter-observation times are exponential distributed;In chapter 4,we do the same work as chapter 3 when the inter-observation times are Erlang?n?distributed.