Asymptotics For The Finite-time Probability With A Constant Rate

It is well known that the ruin theory is an important part of risk theory. In recent years, how to give insurance companies the asymptotic behavior of ruin probability has become a hot issue in risk theory, a lot of papers have been published on the asymptotic estimates of ruin probability of insurance company which is exposed to a stochastic economic environment.Ruin probability is divided into finite and infinite time ruin probability, this article will study the asymptotic behavior of the finite ruin probability with a constant rate. The former can be further divided into uniform and nonuniform asymptotic, here, we will study the nonuniform asymptotic. In this area, Wang(2008) has given two models-the renewal risk model and the general risk model. Recently, Li et al.(2009) has studied the asymptotic behavior of the ruin probability with negatively dependent claims and inter-arrival times. All of previous studies all are under the same distribution, that is too ideal. In practice, the distribution of the claims in insurance company are often different. This paper will study the asymptotic behavior of ruin probability in a wider area with different distributions and negatively dependent claims.In the second chapter, firstly, we will extend the negatively dependent claims under the same distribution, and then study the asymptotic behavior of the ruin probability with different distributions.