Dependent Risk Model With Constant Interest Rate Bankruptcy Probability

The classical risk model is usually investigated without the effect of the interest force, but the interest force is an important factor for the insurance company in actual economic environment. At the same time, in the classical risk model, the claim amounts and the interclaim times are always assumed to be independent. But in practical context, this assumption can be restrictive, so more and more risk models with inter claim-dependent claim sizes have been studied. In this paper, first, we investigate the distributions of the product of two random variables, which are independent. Next, we investigate the ruin probability of the renewal model with interest force. In this model the claim sizes form a sequence of identically distributed random variables with heavy-tailed distribution function.This paper is divided into four chapters according to contents:In Chapter 1, we introduce the context of the product of two random variables, which are independent. Furthermore, we introduce the risk model with constant interest,In Chapter 2, we introduce the definition of heavy-tailed distribution, several impor-tant distribution groups and the relation among of them. And, we also introduce some marks and concepts.In Chapter 3, we follow the work of [2] and extend the class of the distribution of the product of two random variables, which are independent.In Chapter 4, we study the ruin probability for the risk model when the claims obey the same distribution F∈C, furthermore, the claims are quasi-asymptotically indepen-dent. We extend the result of [8], which the claims obey the same distribution F∈ERV.