摘要
利用Girsanov变换,证明了当g是线性生成元时,g期望等价于经典的数学期望,此时,g期望关于一般二元凹函数的Jensen不等式成立,然后采用生成元表示定理,得到了若g期望关于一般二元凹函数的Jensen不等式成立,则生成元是线性的;最后证明了当且仅当g是次线性生成元时,g期望关于二元单调递增凹函数的Jensen不等式成立。
Using Girsanov transformation, the paper presents an attempt to prove that g expectation is equal to the classical expectation when g is a linear generator, thus Jensen＇ s inequality of general bivariate concave function for g expectation holds. Then the paper, by exploring the representation theorem for generators, leads to conclusion that g is linear when Jensen＇ s inequality of general bivariate concave function holds; it is proved that Jensen＇ s inequality of bivariate increasing concave function holds if and only if g is a sublinear generator.
出处
《黑龙江科技学院学报》
CAS
2007年第3期224-226,230,共4页
Journal of Heilongjiang Institute of Science and Technology
基金
国家自然科学基金项目(10671205)
关键词
倒向随机微分方程
g期望
JENSEN不等式
backward stochastic differential equation （BSDE）
g expectation
Jensen inequality
