Study On Some Problems Of Theory Of Index Of Riskiness

This paper mainly studies some problems about the theory of index of riskiness with parameter.In the first chapter,the research background and status of the index of riskiness together with the main research contents of this paper are introduced.In the second chapter,the theory of Arrow-Pratt absolute risk aversion and some re-sults of Aumman-Serrano economic index of riskiness are reviewed.Furthermore,main results of Resta-Marina index of riskiness with parameter are introduced.In the third chapter,axiom definition of index of riskiness with parameter is given.This chapter obtains that any index of riskiness with parameter satisfying axiom defini-tion is a positive multiple of Resta-Marina index of riskiness with same parameter.The relation between utility parameter of constant absolute risk aversion agent and riskiness index with parameter is builded.Furthermore,the equivalent conditions of two relations for agents comparison of risk aversion are established.In the forth chapter,as riskiness of many integral gambles can not be well-defined under the framework of Resta-Marina index of riskiness,the necessary and sufficient conditions for existence of Resta-Marina index of riskiness with parameter are obtained by discussing the acceptance behavior of constant absolute risk aversion agents.Fur-thermore,this chapter proposed a new index of riskiness which extended Resta-Marina riskiness index such that it is well defined on the whole integrable random variable space L~1(?,F,P).More importantly,this extended index of riskiness meets axiom definition,and any non-trivial index of riskiness with parameter defined on L~1(?,F,P)is a positive multiple of this extended index.