Hybrid Atlas models

TL;DR

This paper investigates Atlas-type equity market models with local rank-dependent characteristics, analyzing their stability, ergodic properties, and implications for investment strategies like growth-optimal and universal portfolios.

Contribution

It introduces a novel class of Atlas models with local characteristics that ensure a stable capital distribution and explores their ergodic and ranking properties.

Findings

Models exhibit stable capital distributions.

Analysis of ergodic properties using reflected Brownian motions.

Evaluation of growth-optimal and universal investment strategies.

Abstract

We study Atlas-type models of equity markets with local characteristics that depend on both name and rank, and in ways that induce a stable capital distribution. Ergodic properties and rankings of processes are examined with reference to the theory of reflected Brownian motions in polyhedral domains. In the context of such models we discuss properties of various investment strategies, including the so-called growth-optimal and universal portfolios.