共单调可加g-估价的一些结果

Some Results of g-Evaluation with Comonotonic Additivity

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.