The Study Of Ruin Probability In The Presence Of Large Claims

This thesis is devoted to the study of ruin probability in the presence of large claims which can be described by the distribution of heavy-tailed. We call X or its distribution function is heavy-tailed, if for a non-negative random variablesX, it satisfied thatEetX=00, for every t>0. Heavy-tailed has played an important role in insurance and finance because it can describe large claims. In this paper, the ruin probability with different interest rates is considered. Under the assumptions that the claim-arrival process is non-standard Poisson process and the claimsize is heavy-tailed, some simple asymptotic for formulae of ruin probability are derived. The results we obtained extended the corresponding conclusion of related references for ordinary Poisson risk model. Furthermore extend the model to the case in which the claims are pairwise negatively dependent. Finally, the insurance capital invested in risky asset is considered, and we get an asymptotic of ruin probability for renewal risk model. Currently the study of ruin probability with investment is mainly focused on the constant interest force, while the research about the stochastic risky investment is very little. In the dealing with investments income, we consider the different part of insurance capital have different investment. Hence the interest rates are most likely different. So the model we established seems to be more realistic, but it also increased the difficulty of the study. Take the different rates into account is one innovation of this paper. It plays an important role into guide the insurer to measure the risk and management about the asset income.We discussed the issue of ruin of insurance companies, it aims to prevent insurer from ruin or to reduce the probability of ruin. Although in reality, this case of ruin doesn't mean that the companies would immediately close down, it can remind the insurer to add fund to cope with the sudden insurance liability, as well it have a direct reference guide for the financial early-warning system and the department of insurance supervision to design some regulation indexes.