Model-free portfolio theory: A rough path approach

doi:10.1111/mafi.12376

	Model-free portfolio theory: A rough path approach
	Allan, Andrew L.1; Cuchiero, Christa 2; Liu, Chong3 ; Proemel, David J.4
	2023
发表期刊	MATHEMATICAL FINANCE
ISSN	0960-1627
EISSN	1467-9965
发表状态	已发表
DOI	10.1111/mafi.12376
摘要	Based on a rough path foundation, we develop a model-free approach to stochastic portfolio theory (SPT). Our approach allows to handle significantly more general portfolios compared to previous model-free approaches based on Follmer integration. Without the assumption of any underlying probabilistic model, we prove a pathwise formula for the relative wealth process, which reduces in the special case of functionally generated portfolios to a pathwise version of the so-called master formula of classical SPT. We show that the appropriately scaled asymptotic growth rate of a far reaching generalization of Cover's universal portfolio based on controlled paths coincides with that of the best retrospectively chosen portfolio within this class. We provide several novel results concerning rough integration, and highlight the advantages of the rough path approach by showing that (nonfunctionally generated) log-optimal portfolios in an ergodic Ito diffusion setting have the same asymptotic growth rate as Cover's universal portfolio and the best retrospectively chosen one.
关键词	Cover's universal portfolio log-optimal portfolio model uncertainty pathwise integration rough path stochastic portfolio theory
URL	查看原文
收录类别	SCI ; SCOPUS ; SSCI
语种	英语
资助项目	Schweizerischer National fonds zur Forderung der Wissenschaftlichen Forschung["200021_184647","P2EZP2_188068"] ; Austrian Science Fund["Y 1235","I 3852"] ; Vienna Science and Technology Fund[MA16-021]
WOS研究方向	Business & Economics ; Mathematics ; Mathematical Methods In Social Sciences
WOS类目	Business, Finance ; Economics ; Mathematics, Interdisciplinary Applications ; Social Sciences, Mathematical Methods
WOS记录号	WOS:000919768500001
出版者	WILEY
引用统计
文献类型	期刊论文
条目标识符	https://kms.shanghaitech.edu.cn/handle/2MSLDSTB/282125
专题	数学科学研究所_PI研究组(P)_刘翀组
通讯作者	Cuchiero, Christa
作者单位	1.Univ Durham, Durham, England 2.Univ Vienna, Vienna, Austria 3.ShanghaiTech Univ, Shanghai, Peoples R China 4.Univ Mannheim, Mannheim, Germany
推荐引用方式 GB/T 7714	Allan, Andrew L.,Cuchiero, Christa,Liu, Chong,et al. Model-free portfolio theory: A rough path approach[J]. MATHEMATICAL FINANCE,2023.
APA	Allan, Andrew L.,Cuchiero, Christa,Liu, Chong,&Proemel, David J..(2023).Model-free portfolio theory: A rough path approach.MATHEMATICAL FINANCE.
MLA	Allan, Andrew L.,et al."Model-free portfolio theory: A rough path approach".MATHEMATICAL FINANCE (2023).