  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.
