Random Interest Rate Sector, Since The Bankruptcy Probability Of The Regression Model

Ruin probability is a main research hotspot in risk theory. Many generalized classical risk models have been studied widely such as adding the rates of interest into models, stochastic premiums etc. In this thesis, we mainly study the ruin probabilities in finite time and the ruin probabilities in infinite time in two generalized discrete time risk models. The effects of interest and the dependent situation of both the aggregate claims and the aggregate premiums on the ruin probabilities in the models are considered. We create the risk models, in which the rates of interest are assumed to have a dependent autoregressive structure of order 2 and their aggregate premiums and aggregate claims each have a dependent autoregressive structure of order 1. Upper bounds for the ruin probabilities are derived by an improved renewal recursive technique.In chapter 1, we introduce the classical risk model and the development of ruin theory.In chapter 2, under the assumptions of dependent structures of the rates of interest, the aggregate claims and the aggregate premiums as above, a discrete time risk model that considered payments and claims at the end of each period is set up and upper bounds for the ruin probability in finite time and the ruin probability in infinite time are derived.In chapter 3, under the same assumptions as chapter 2, a discrete time risk model that considered payments at the beginning of each period and claims at the end of each period is set up and upper bounds for the ruin probability in finite time and the ruin probability in infinite time are derived.In chapter 4, we compare the upper bounds for the ruin probabilities in chapter 2 with chapter 3.In chapter 5, we point out the direction of further expansion.