共单调次可加F-期望及相关性质  

F-expectation with Comonotonic Subadditivity and Related Properties

作　　者：孙倩怡[1] 石学军[1] 江龙[1] 杨莹[1] 

机构地区：[1]中国矿业大学理学院,江苏徐州221116

出　　处：《徐州工程学院学报（自然科学版）》2010年第4期1-4,12,共5页Journal of Xuzhou Institute of Technology(Natural Sciences Edition)

基　　金：国家自然科学基金资助项目(10971220);中央高校基本科研业务费专项资金资助项目(2010LKSX04)

摘　　要：给出了共单调次可加F-期望的概念,证明了当共单调次可加F-期望满足一定条件时,其不仅是正齐次的,条件F-期望也是正齐次的,且条件F-期望关于单调增凸函数的Jensen不等式成立;进一步地,如果F-期望还是凸的,那么条件F-期望满足次可加性,且条件F-期望的Jensen不等式一般成立.如果共单调次可加F-期望对于示性函数满足一定条件,则该F-期望能被相应的Choquet期望所控制.The paper gives the definition of F-expectation with comonotonic subadditivity,and shows that it is positively homogeneous when satisfied with certain conditions,that the conditional F-expectation is also positively homogeneous,and that the Jensen＇s inequality holds for the conditional F-expectation with the increasing convex functions.Furthermore,if the F-expectation is also convex,then the conditional F-expectation satisfies the property of subadditivity,and the Jensen＇s inequality holds in general for the conditional F-expectation.It is dominated by the corresponding Choquet expectation,when the expectation with comonotonic subadditivity meets some conditions for the indicator functions.

关 键 词：共单调次可加 F-期望 条件F-期望 Choquet期望 JENSEN不等式 

分 类 号：O221.6[理学—运筹学与控制论]