| This thesis mainly studies related problems in the theory of Aumann-Serrano(AS)economic index of riskiness.In the first chapter,we mainly introduce the research background and status of the index of riskiness,and the contents of this thesis.In the second chapter,we mainly introduce the preparatory knowledge required,including the definitions and properties of AS economic index of riskiness,risk sensitive value measure and inner rate of risk aversion.In the third chapter,we mainly study the properties of AS performance index of three types of gambles,and the relationship between AS performance index and inner rate of risk aversion(IRRA).When the gambles obey binomial distribution,normal distribution and uniform distribution,using Matlab to draw and analyze the implicit equation images of IRRA and AS performance index,and calculate the value of the solution,exploring the expression of the AS performance index in normal distribution.Studying the changing law of AS performance index,and proving it is a better way to obtain the value of AS performance index through IRRA’s implicit equation.In the fourth chapter,we mainly study the definitions and properties of the risk sensitive value measure and inner rate of risk aversion of gambles on quadratic utility function.The expression form and the condition of existence and uniqueness of the risk sensitive value measure based on quadratic utility function are given;giving the condition of the risk sensitive value measure is convex(concave)risk measure;giving the definition and expression form of the IRRA of quadratic utility,discussing the condition of existence and uniqueness when it is positive and negative.When the gambles obey binomial distribution,normal distribution and uniform distribution,using Matlab to draw and analyze the IRRA implicit equation image of the quadratic utility function,calculate the value of the solution,verify the sufficient condition of the uniqueness of IRRA of quadratic utility function.Studying the changing law of IRRA of quadratic utility function,proving that there is an opposite size relationship between the AS performance index and IRRA of quadratic utility function... |
