Non-additive Measure Choquet Premium Pricing

In the area of international economy,the study of non-additive measure is a hot issue. Many mathematician and economiasts have applied non-additive probability measure to measure the indefinity. As we all know,there exists the following integral relationship between mathematics expectation and the correspondent probability in classical probability:In 1995, Choquet expanded this relationship as integaled function to be non-additive measure—capacity:and claimed this expression Choquet integral.Choquet integral is an integral that has been developed lately about non-dditive measure in the theory of definity.It has been widely used in insurance,economics, finance and game theory.Insurance is an effective method of dealing with risk and indefinity in commodity societies. The economics theory on risk and indefinity is very fundamental in insurance economy.During the last few decades,expectation theory has made great contribution to the understanding of risk and indefinity economy.For instance,it is used to determine:(l) the optimal of insurance policy.(2) the optimal insurance policy for major accident.(3) the optimal insurance profit for storage and the outcome of insurance pricing.Many efforts have been devoted to constructing an ideal model of risk loss claimed priced in this area due to Arrow's contribution(1953) 50 years before.50 years after that ,people have proposed many models.Yarri(1987) proposed the opinion of person insurance preferability.In Yarri's theory,it is distorted probabilty towards risk.Wang(1997) proposed a set of comparatively strict characterized prium pricing principle with Choquet integral as its theoretical basis.It says:Assuming risk assemble X includes all random variables of Bernoulli (u) and if marketing insurancing price function H satisfies the quality of economic significance,then (?)distorted function g s.t.which 1 is degenerate random variable,so as to probability 1 foundation.Then the insurancing pric of risk X can be considered as its expectation on non-additive measure gap .As we all know, in classic expectation theory. If random variable X, Y are independent, then E'fXF] = ￡[X].El[Y].Let us turn to the following issues:(1) Risk XY being independent and on the premise of markrt non-arbitr'age,what should g satisfy if there is H[XY] = H[X)H[Y)1(2) How to make insurancing policy I to make policy holders to get maximal profit for general compound risk XY ?The present paper argues elaborately and provide tentative result around the above questions.The five sections in this paper:Chapter one presents the theoretical background of this subject.Chapter two elaborates on Wang's insurancing pricing priciple,including the property insurancing pricing function shouldposess in market.Chapter three deals with insurance price in Choquet integral expression and compound Bernoulli, including some contrbution of Greco,Wang.Chapter four and five are the author's main result.Chapter four: The author provides compound risk Choquet integral expression and its application in independent and comonotonic situations.Chapter five: The author provides the conditions compound risk XY and optimal policy I should satisfy.