  In this paper we develop a concrete and fully implementable approach to the
optimization of functionally generated portfolios in stochastic portfolio
theory. The main idea is to optimize over a family of rank-based portfolios
parameterized by an exponentially concave function on the unit interval. This
choice can be motivated by the long term stability of the capital distribution
observed in large equity markets, and allows us to circumvent the curse of
dimensionality. The resulting optimization problem, which is convex, is
flexible as various regularizations and constraints can be imposed on the
generating function. We prove that the optimization problem is well-posed and
provide a stability estimate in terms of a Wasserstein metric of the input
measure. We then give a careful treatment of its discretization and the
optimization algorithm. Finally, we present empirical examples using CRSP data
from the US stock market.
