g-期望框架下Choquet期望在风险度量中的应用  

Choquet Expectations and their Applications about Risk Measures in the Framework of g-Expectations

作　　者：杨志[1] 

机构地区：[1]青岛理工大学基础部,山东临沂273400

出　　处：《贵州大学学报（自然科学版）》2015年第4期9-11,50,共4页Journal of Guizhou University:Natural Sciences

基　　金：国家自然科学基金项目资助(10971220)

摘　　要：本文在倒向随机微分方程(BSDE)框架下研究由g-容度诱导的Choquet期望在风险度量领域的相关性质,得到Choquet期望表示为一致风险度量的充分必要条件,即g-容度具有二次交替性。在g-容度满足二次交替的条件下,得到当g-期望受控于Choquet期望时,g-期望关于示性函数具有超齐次性与次可加性。The relationship between Choquet Expectations and risk measure in the framework of backward sto- chastic differential equation was studied. The result that Choquet expectations expressed in the form of coherent risk measures was obtained and the necessary and sufficient condition that g-capacity is 2-alternating was found. It is proved that if g-capacity is 2-alternating and g-expectation is dominated by the Choquet expectation then g- expectation satisfies superpositively homogeneous and sub-additive conditions for all indicator functions.

关 键 词：倒向随机微分方程 G-期望 Choquet期望 一致风险度量 凸风险度量 

分 类 号：O211.6[理学—概率论与数理统计]