分布约束的最优多重停时：Root型解

中文摘要 AI 辅助

我们研究Bayraktar和Miller（《数学金融》，2019）以及Beiglböck等人（《概率理论与相关领域》，2018）提出的分布约束最优停时问题。受多边际Skorokhod嵌入问题（SEP）及数学金融应用的启发，我们将其一类解推广至多边际情形。首先，我们给出该解的概率刻画：作为时间反向过程首次击中障碍集的时刻，与Cox等人（《概率理论与相关领域》，2019）的思路一致。随后，我们利用鞅不等式论证证明最优性结果，该结果扩展了Beiglböck等人（《概率理论与相关领域》，2018）所考虑的成本函数类型。

英文摘要

We consider the distribution-constrained optimal stopping problem introduced by Bayraktar and Miller (Mathematical Finance, 2019) and Beiglbock et al. (PTRF, 2018). Motivated by the multi-marginal Skorokhod embedding problem (SEP) and applications in financial mathematics, we generalize the Root-type solution to the multi-marginal case. The key difficulty is that the associated stopping barriers need not be ordered, so the problem in general cannot be reduced to a sequence of one-marginal problems. First, we give a probabilistic characterization in terms of sequential optimal stopping for an auxiliary time-reversed process, in the same spirit as Cox et al. (PTRF, 2019). Then, we prove the optimality of this construction by martingale arguments for a general class of reward functions, including multi-marginal versions of all examples in Beiglbock et al. (PTRF, 2018) as special cases.

发表机构

• The Hong Kong University of Science and Technology（香港科技大学）

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