Ruin Probability Of A Class Of Dependent Risk Model

In the Sparre Andersen model, the distributions of Tk and Xk are independent, many real-world situations for such an assumption is inappropriate.In this paper, we expand the model of Ambagaspitiya (2009) and consider the pre-mium income pays in the beginning of the year and the claim is paid in the end of the year, the model with dependent claim sizes and claim occurrence times under the influ-ence of interest rate and inflation rate. We obtain explicit expressions for the ultimate ruin probability. As in a certain period of time, interest rate and inflation rate are usually more stable, therefore, we only consider interest rate and inflation rate are constant.The thesis is divided into four sections according to contents:In the first chapter, we introduce the development of the bankruptcy risk model from independent model to dependent risk model and the general process of risk model. We also introduce the model of this paper, the model is given by:In the second chapter, we outline the method used to obtain the Laplace transform of the survival probability. We obtain the relationship between the Laplace transform of the survival probability and its moment generating function:In the third chapter, we mainly consider the model with dependent claim sizes and claim occurrence times under the influence of interest rate and inflation rate. The bivariate gamma distribution with the following moment generating function: We obtain explicit expressions for the ultimate ruin probability: In the fourth chapter, we consider the model with dependent claim sizes and claim oc-currence times under the influence of interest rate and inflation rate, which obeys Cheriyan and Ramabhadran's bivariate gamma distribution, this bivariate gamma distribution with the following moment generating function: We obtain explicit expressions for the ultimate ruin probability:In order to facilitate readers to read and check, in this paper we give two appendix: appendix A and appendix B. Appendix A will be used in the second chapter, Appendix B will be used in the third and the fourth chapter. Readers can read this paper by the two appendix at any time.