A Filtered Version of the Bipolar Theorem of Brannath and Schachermayer
A Filtered Version of the Bipolar Theorem of Brannath and Schachermayer
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Brannath 和 Schachermayer 双极定理的过滤版本
DOI：
10.1023/a:1013885121598
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发表时间：
2007
影响因子：
0.8
通讯作者：
Gordan Zitkovic
中科院分区：
文献类型：
--
作者：
Gordan Zitkovic
将Kramkov和Schachermayer（12）的双极定理推广到滤波概率空间上的非负càdlàg上鞅空间。在这种情况下，我们将分叉凸性的概念表述为凸性的类比。作为证明我们的主要结果的中间步骤，我们建立了双极定理的条件版本。在数学金融学的一个应用中，我们描述了Kramkov和Schachermayer（12）的效用最大化问题的对偶过程集的结构，并给出了不完全半鞅市场中可容许消费过程的预算约束表征。
We extend the Bipolar Theorem of Kramkov and Schachermayer(12) to the space of nonnegative càdlàg supermartingales on a filtered probability space. We formulate the notion of fork-convexity as an analogue to convexity in this setting. As an intermediate step in the proof of our main result we establish a conditional version of the Bipolar theorem. In an application to mathematical finance we describe the structure of the set of dual processes of the utility maximization problem of Kramkov and Schachermayer(12) and give a budget-constraint characterization of admissible consumption processes in an incomplete semimartingale market.