HARRY MARKOWITZ [1952, 1956, 1959] developed a theory of portfolio selection based on
the optimization of a quadratic function subject to linear constraints. His work led to the …

… This theory was introduced by ER Fernholz in the papers (Journal of … Stochastic Portfolio
Theory (SPT), as we currently think of it, began in 1995 with the manuscript “On the diversity of …

In this chapter we introduce the basic definitions for stocks and portfolios, and prove preliminary
results that are used throughout the later chapters. The mathematical definitions and …

A first-order model for a stock market assigns to each stock a return parameter and a variance
parameter that depend only on the rank of the stock. A second-order model assigns these …

We consider a setup in which infinitely lived households face idiosyncratic investment risk
and show that in this case the equilibrium distribution of wealth becomes increasingly right-…

Atlas-type models are constant-parameter models of uncorrelated stocks for equity markets
with a stable capital distribution, in which the growth rates and variances depend on rank. …

… the long term, however, this simulated market tends to concentrate itself into a single giant
stock, even if all the stocks have the same expected compound growth rate (see Fernholz […

We provide simple, easy-to-test criteria for the existence of relative arbitrage in equity markets.
These criteria postulate essentially that the excess growth rate of the market portfolio, a …

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 …

An equity market is called “diverse” if no single stock is ever allowed to dominate the entire
market in terms of relative capitalization. In the context of the standard Itô-process model …