2021/10/26 by David Itkin, Martin Larsson, Itkin, David +1 · 3 citations
Economics, Econometrics and Finance · #60J60 #91G15 #FOS: Economics and business #FOS: Mathematics #Financial Markets and Investment Strategies #Financial Risk and Volatility Modeling #Mathematical Finance (q-fin.MF) #Primary 60G44 #Probability (math.PR) #Secondary 60J46 #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2110.14046
openalex publication_date 2021/10/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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) unleveraged and explicit 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.