OPEN MARKETS AND HYBRID JACOBI PROCESSES

• 成果类型: Article
• 署名作者: Itkin, David; Larsson, Martin
• 署名单位: Imperial College London; Carnegie Mellon University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/23-AAP2030
• 发表日期: 2024
• 页码: 2940-2985
• 关键词: robust maximization

摘要

We propose a unified approach to several problems in stochastic portfolio theory (SPT), which is a framework for equity markets with a large number d of stocks. Our approach combines open markets , where trading is confined to the top N capitalized stocks as well as the market portfolio consisting of all d assets, with a parametric family of models which we call hybrid Jacobi processes . We provide a detailed analysis of ergodicity, particle collisions, and boundary attainment, and use these results to study the associated financial markets. Their properties include (1) stability of the capital distribution curve and (2) explicit and not artificially leveraged growth optimal strategies. The sub -class of rank Jacobi models are additionally shown to (3) serve as the worst -case model for a robust asymptotic growth problem under model ambiguity and (4) exhibit stability in the large -d limit. Our definition of an open market is a relaxation of existing definitions which is essential to make the analysis tractable.