Optimal Stopping via Distribution Regression: a Higher Rank Signature Approach
2023-04-04
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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
DOIarXiv:2304.01479
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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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