Studies On The Structure Of Risks

Risk theory is a hot spot in modern actuarial science and risk structure is an important content in risk theory.On the assumption that risk is mutually independent, Classical risk theories give priority to stochastic risk models of insurance and survival or ruin probability within a limited time.In stochastic risk models,we consider mostly continual time risk models,especially compound Poisson procession risk models, discrete risk models are seldom treated,but discrete risk models are easier to perceive and more applicable.When treating discrete risk models,we often mention a compound binomial risk model whose characteristic is that the mean of claim numbers is greater than the variance of claim numbers,a compound binomial risk model is suitable for homogeneous policies assemblages,has been discussed.Actually policies assemblages have more or less non-homogeneity,a compound negative binomial risk model is more suitable for non-homogeneous policies assemblages than a compound binomial risk model and the property is that the variance of claim numbers is greater than the mean of claim numbers.This thesis Studies a compound negative binomial risk model whose formula of ultimate ruin probability has been proved by applying discrete martingale theory,the method is different form others references.We construct a compound negative binomial risk model with a completely stochastic premium where the premium of every policy and the number of insure charges at per unit time are random variables.This paper discusses some properties of a compound negative binomial risk model with a completely stochastic premium.By applying discrete martingale theory,this article proves the formula of ultimate ruin probability and the Lundberg inequality.When only considering a policy whose premium and claim are independent each other,we can apply all sorts of risk models.But every insurer has a lot of policies whose premium and claim don't accord with existing risk models,this results that we can not apply the classics risk theories and use value at risk(VaR)to study a portfolio. Insures reinsure a policy whose loss exceeds the insurer's anticipation.Some scholars have studied an asset's VaR and stop-loss premium and some special portfolio's VaR, this thesis has discussed arbitrary asset portfolio's VaR and stop-loss premium, analytical expressions for risk value and stop-loss premiums of sums of independent random variables have been given.At finial,function convex order of non—negative random variables is introduced for random assets' VaR,the conclusion is that portfolio assets VaR can not exceed the sum of individual asset VaR,and the upper of portfolio is also given.Risk structure problem is an important aspect of risk theory and is important significance for controlling risk of financial enterprises.This thesis has studied a new risk model which is more in line with the reality of insurers and arbitrary assets' portfolio's VaR,we study risk structure problem to guard against the occurrence of bankruptcy and our results are the gist for controlling risk of financial enterprises.