标题： Brannath 和 Schachermayer 的双极定理的过滤版本 显示英文标题

标题： A filtered version of the bipolar theorem of Brannath and Schachermayer

摘要： 我们将 Brannath 和 Schachermayer（1999）的双极定理推广到过滤概率空间上的非负右连续有界上鞅空间。我们在此背景下引入叉凸性作为凸性的类比概念。在证明我们的主要结果的过程中，我们建立了该双极定理的一个条件版本。在金融数学的应用中，我们描述了 Kramkov 和 Schachermayer（1999）提出的效用最大化问题的对偶过程结构，并给出了不完备半鞅市场中可接受消费过程的预算约束特征化。 显示英文摘要

摘要： We extend the Bipolar Theorem of Brannath and Schachermayer (1999) to the space of nonnegative cadlag 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 (1999) and give a budget-constraint characterization of admissible consumption processes in an incomplete semimartingale market.