Filtration-consistent nonlinear expectations and related g-expectations
Filtration-consistent nonlinear expectations and related g-expectations
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DOI：
10.1007/s004400100172
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发表时间：
2002-05
影响因子：
2
通讯作者：
F. Coquet;Ying Hu;J. Mémin;S. Peng
中科院分区：
文献类型：
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作者：
F. Coquet;Ying Hu;J. Mémin;S. Peng
从非线性期望的一般定义出发，把非线性期望看作是保持单调性和常数的算子，在相当一般的假设下，我们导出了条件非线性期望和非线性鞅的概念。我们证明了任何这样的非线性鞅都可以表示为倒向随机方程的解，特别是允许连续路径。换句话说，它是鞅。
From a general definition of nonlinear expectations, viewed as operators preserving monotonicity and constants, we derive, under rather general assumptions, the notions of conditional nonlinear expectation and nonlinear martingale. We prove that any such nonlinear martingale can be represented as the solution of a backward stochastic equation, and in particular admits continuous paths. In other words, it is ag-martingale.