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Optimal Stopping via Distribution Regression: a Higher Rank Signature Approach | |
2023-04-04 | |
状态 | 已发表 |
摘要 | Distribution Regression on path-space refers to the task of learning functions mapping the law of a stochastic process to a scalar target. The learning procedure based on the notion of path-signature, i.e. a classical transform from rough path theory, was widely used to approximate weakly continuous functionals, such as the pricing functionals of path--dependent options' payoffs. However, this approach fails for Optimal Stopping Problems arising from mathematical finance, such as the pricing of American options, because the corresponding value functions are in general discontinuous with respect to the weak topology. In this paper we develop a rigorous mathematical framework to resolve this issue by recasting an Optimal Stopping Problem as a higher order kernel mean embedding regression based on the notions of higher rank signatures of measure--valued paths and adapted topologies. The core computational component of our algorithm consists in solving a family of two--dimensional hyperbolic PDEs. |
关键词 | Optimal Stopping Problem Adapted Weak Topology Higher Rank Signatures Kernel Regression |
DOI | arXiv:2304.01479 |
相关网址 | 查看原文 |
出处 | Arxiv |
WOS记录号 | PPRN:54058516 |
WOS类目 | Mathematics |
资助项目 | Munich Data Science Institute[EP/S026347/1] |
文献类型 | 预印本 |
条目标识符 | https://kms.shanghaitech.edu.cn/handle/2MSLDSTB/348370 |
专题 | 数学科学研究所_PI研究组(P)_刘翀组 |
作者单位 | 1.Tech Univ Munich, Munich Data Sci Inst, Munich, Germany 2.Alan Turing Inst, London, England 3.Univ Oxford, Oxford, England 4.ShanghaiTech Univ, Shanghai, Peoples R China 5.Imperial Coll London, London, England |
推荐引用方式 GB/T 7714 | Horvath, Blanka,Lemercier, Maud,Liu, Chong,et al. Optimal Stopping via Distribution Regression: a Higher Rank Signature Approach. 2023. |
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