Open Markets and Hybrid Jacobi Processes

TL;DR

This paper introduces a unified framework combining open markets and hybrid Jacobi processes in Stochastic Portfolio Theory, analyzing their stability, ergodicity, and growth strategies, with implications for large equity markets.

Contribution

It develops a new model class called hybrid Jacobi processes and analyzes open markets, providing insights into stability, growth, and robustness in large-scale equity markets.

Findings

Stable capital distribution curves in the models

Explicit growth optimal strategies identified

Hybrid Jacobi processes serve as worst-case models under ambiguity

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) 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.