倒向随机微分方程中生成元g的经济含义

The Economic Meanings of Generators in Backward Stochastic Differential Equations

将倒向随机微分方程看作金融市场中的一个定价机制,而该机制具体体现就是生成元g.本文通过经典的Black-Scholes模型探讨了生成元g的经济含义,首次提出了生成元g的表达式中含有折现的概念,同时详细分析并说明了不同的生成元g可以反应同一未定权益价格过程的不同形态.最后结合上面的讨论给出了关于一定形式的生成元g的类Jensen不等式性质.

Taken backward stochastic differential equation as a mechanism of pricing in financial market, the decisive part is the generator. Here some economic meanings of the generator are discussed in virtue of the classic Black-Scholes model. The idea is first proposed that the expression of a generator includes the notation of discount. Meanwhile, for the same price process of a contingent claim, different generators can respond its different forms. Combined with the above discussion, a similar Jensen＇s inequality about the generator with a fixed form is given finally.