共单调次可加g-估价与生成元g之间的关系

Relationship between g-evaluation with comonotonic subadditivity and generator g

为了丰富g-估价的理论研究,利用生成元的唯一性定理和表示定理,在Lipschitz条件和g(t,0,0)=0条件下,证明了如果生成元g是凸函数,则对于某一类g-估价满足共单调次可加性当且仅当g-估价系统满足共单调次可加性,当且仅当生成元g是次可加的;当布朗运动的维数为1时,给出了g-估价是共单调次可加的一个必要条件。该结果拓展了具有共单调次可加性的g-期望的已有结论。

This paper is aimed at enriching the theoretical research on g - evaluation by using the generator uniqueness theorem and representation theorem,under the conditions of Lipschitz g（t,0,0） = 0.The research leads to the proof that if the generator g is convex function,then a class of g - evaluation satisfies comonotonic subadditivity if and only if g - evaluation system is comonotonic subadditive if and only if g is subadditive.When the dimension of the brownian motion is one,it gives a necessary condition for the g - evaluation with comonotonic subadditivity.These results expand the conclusions for the g - expectation with comonotonic subadditivity.