Open markets and hybrid Jacobi processes

David Itkin and Martin Larsson

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

Abstract: 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.

Keywords: boundary attainment; Dirichlet forms; growth optimality; open markets; Poisson–Dirichlet distribution; robust finance; Stochastic Portfolio Theory (search for similar items in EconPapers)
JEL-codes: C1 (search for similar items in EconPapers)
Date: 2024-06-01
References: Add references at CitEc
Citations:

Published in Annals of Applied Probability, 1, June, 2024, 34(3), pp. 2940-2985. ISSN: 1050-5164

Downloads: (external link)
https://researchonline.lse.ac.uk/id/eprint/141433/ Open access version. (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:ehl:lserod:141433

Access Statistics for this paper

More papers in LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library LSE Library Portugal Street London, WC2A 2HD, U.K.. Contact information at EDIRC.
Bibliographic data for series maintained by LSERO Manager ().