Estimates Of Ruin Probabiliyties Based On The Heavy Tail Conditions

It is well known that risk theory, as an significant branch of the applied probability theory, is an important part in financial insurance, which not only has important theoretical research value, but also has a guiding significance on the actual work of financial insurance. Due to the large amount of risk has the great influence of operating conditions to insurance company claim for compensation, risk theory of catastrophe is more and more concerned. In mathematics, if random variables will be able to describe this risk, that subject to a kind of heavy tail distribution, so the heavy tail distribution model draws the attention of the people now. This paper gives the definitions and features of common subclass of heavy-tailed distribution, which mainly researches the heavy-tailed random variables in the nature of how to solve the ruin probability problems of insurance companies. In this thesis we are interested in the impact of economic and financial factors, such as interest rate and investment return on insurance business. It has a very strong practical significance to estimate the risk of insurance and process risk. Specific content is divided into the following three parts:Firstly, in order to have a comprehensive understanding for people to heavy-tailed, this paper summarizes the characteristics of subclasses of heavy-tailed and their relations based on the current research status of tail distribution function in domestic and foreign, then help for further theory research and applied research of heavy-tailed distribution.Secondly, in discrete time risk model, assuming that individual net risk is related with the distribution, and the interest rate of the random changes in different claim time intervals. The rule changes the nature of the non-normal distribution, gets the approximate expression for the ruin probability. And then in a given certain assumptions of interest rates, by using the method of weighted sum of random variables and the stability of Subexponential distribution, we obtain approximate expression of the finite time ruin of insurance company.Then, consider surplus of the premium of the insurance company income invest in risky assets, this paper established a sequence of independent and identically distributed random pairs following a common bivariate Farlie-Gumbel-Morgenstern distribution with marginal distribution functions, using conditional probability of two random variables insurance risk and financial risk is boundedness, we derive a general asymptotic formula for the finite-time ruin probability. Lastly, in order to better explain the practicality of papers, this paper gives some bankruptcy cases analysis the subclass of Subexponential distribution.