共单调可加g-估价的一些结果  

Some Results of g-Evaluation with Comonotonic Additivity

作　　者：朱冬芸[1] 江龙[1] 田德建[1] 冯世强[2] 

机构地区：[1]中国矿业大学理学院,江苏徐州221116 [2]西华师范大学数学与信息学院,四川南充637002

出　　处：《中国矿业大学学报》2010年第5期790-794,共5页Journal of China University of Mining & Technology

基　　金：国家自然科学基金项目(10971220);全国优秀博士学位论文作者专项资金项目(200919);江苏省"青蓝工程"计划

摘　　要：研究了由倒向随机微分方程诱导的未定权益的价格系统理论——g-估价理论,分析了具有共单调可加性的g-估价的一些性质;利用具有共单调可加性的算子特征、倒向随机微分方程解关于终值的连续性以及倒向随机微分方程生成元的表示定理,证明了如果一个g-估价满足共单调可加性,则它也满足正齐次性,并且相应的生成元g关于变量y,z是正齐次的,同时有g(t,0,0)≡0.进一步地,若布朗运动的维数为1,利用生成元表示定理,得到了生成元g关于变量y,z是可加的一个充分条件,并由此得到了生成元g的表达形式.Some properties of g-evaluation with comonotonic additivity were studied.Based on the characterization of the operator with comonotonic additivity,the continuity of solutions of backward stochastic differential equations with respect to terminal data and the representation theorem for generators of backward stochastic differential equations,if a g-evaluation satisfies the property of comonotonic additivity,then it also satisfies the positively homogeneous property,the corresponding generator g must be positively homogeneous with respect to variables y and z and g（t,0,0）≡0.Furthermore,if the dimension of brownian motion is one,based on the representation theorem for generators of backward stochastic differential equations,a sufficient condition for generator g is additive with respect to variables y,z is presented.At the same time,the explicit formation of generator g is proposed.

关 键 词：倒向随机微分方程 G-期望 条件G-期望 g-估价 共单调可加性 

分 类 号：O211.6[理学—概率论与数理统计]