Stochastic portfolio theory is a framework to study large equity markets over long time horizons. In such settings investors are often confined to trading in an “open market” setup consisting of only assets with high capitalizations. In this work we relax previously studied notions of open markets and develop a tractable framework for them under mild structural conditions on the market. Within this framework we also introduce a large parametric class of processes, which we call rank Jacobi processes. They produce a stable capital distribution curve consistent with empirical observations. Moreover, there are explicit expressions for the growth-optimal portfolio, and they are also shown to serve as worst-case models for a robust asymptotic growth problem under model ambiguity. Lastly, the rank Jacobi models are shown to be stable with respect to the total number of stocks in the market. Time permitting, we will show that, under suitable assumptions on the parameters, the capital distribution curves converge to a limiting quantity as the size of the market tends to infinity. This convergence result provides a theoretical explanation for an important empirically observed phenomenon.

This talk is based on joint work with Martin Larsson.