Studies On The Structure Of Risks

In 1965,L.A.Zadeh published ground-breaking thesis about "fuzzy sets",creating a new branch of mathematics - Fuzzy Math,formed a system of fuzzy theory.This theory is the method used symbols to express fuzzy concepts and fuzzy objects,and currently most widely used in a systematic approach fuzzy theory,and currently on the basis of fuzzy theory.It have extended classical mathematics basic math,especially in statistics,economics and other fields widely used.Since R.Viertl put statistics into the introduction of fuzzy math,many scholars have carried fuzzy Bayes research out from different angles.At present,the main contents study is the use of fuzzy Bayes methods of parameter estimation,interval estimation,hypothesis testing,etc.Look from the existing literature,fuzzy Bayes methods mainly concentrated in the exponential distribution,binomial distribution and other parameters of the distribution of symmetric function.In this paper,about fuzzy sense,by choosing an asymmetric LINEX loss function,we discuss bilateral truncated-type distributions of the parameters of membership function of Bayes estimates and Bayes estimates of experience,and give their estimate of permissible, and discussed the sample information is divided into both clear and vague cases the assumption of multiple fuzzy truncated distribution vague Bayesian hypothesis testing methods,and finally through the numerical example to verify the reasonableness of the conclusion.Classical statistics on the economics plays an important role,in particular,the risks are the theoretical study.Fuzzy statistical theory applied to the risks,is one of the important task of fuzzy math promotion.Some domestic scholars have fuzzy math applied to portfolio theory,risk assessment theory and so on,have been very good results.However,its application to the theory of bankruptcy is even less.In this paper, we put stochastic model of two dual-risk model to the fuzzy problem of insolvency within the meaning of two dual-model stochastic model of bankruptcy.That is,the volume of premiums collected and the amount claimed and interest rates are different between the membership function relationship,and between interest rates and inflation with a fuzzy linear autoregressive structure of the bankruptcy problem.We have been related to inflation and interest rates and the bankruptcy probability of fuzzy integral expression,followed by analysis of the use of martingale methods of fuzzy probability of bankruptcy classic Lundberg upper bound.Finally we give a classic than the Lundberg upper bound more precise upper bound.Moreover,this sector are on the company's actual operations conform to use.Fuzzy Math in the application has attempted to promote.