Estimate For Finite Time Ruin Probability With Insurance And Financial Risks

It is well known that the ruin theory is the key component of the risk probability and much attention has been paid to issues of ruin theory.One of the hot issues of this research is the asymptotic estimation of ruin probability of an insurer.Recently,a lot of papers have been published on the asymptotics estimates of ruin probability of an insurer who is exposed to a stochastic economic environment.This enviroment has two kinds of risk,which were called by Norberg(1999) as insurance risk and financial risk, respectively.Tang and Tsitsiashvili2003,2004 obtained several precise asymptotics estimates for the finite time ruin probability,in which insurance risk belongs to the intersection of the long-tailed distribution class and dominated-variation distribution class.Later,Chen and Xie(2005) used a simpler method to prove the same result under a weaker assumption on the financial risk.In this paper,we give estimates for the finite tirne ruin probability with insurance and financial risks for two cases.In the second chapter of this paper,we discuss the case of dominated varying-tailed insurance risks,and obtain asymptotic upper bound and lower bound for the ruin probability, where for the asymptotic upper bound,we completely relieve the restrictions of mutually independence and any dependence on insurance risks;and for the lower bound,we only need the insurance risks have a weak positive association structure.Furthermore, in the third chapter of this paper,we discuss the case of independence insurance risks with non-dominated varying-tail;we gain some asymptotic equivalent relationships for the run probability.All above researches require that the financial risks have an independent identically distributed(i.i.d.) structure.All results of this paper and Chen and Xie(2005)'s result give a quite complete products.