Functional Portfolio Optimization in Stochastic Portfolio Theory

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 optimize over family rank-based parameterized by an exponentially concave function on unit interval. This choice can be motivated long term stability capital distribution observed large equity markets allows us circumvent curse dimensionality. resulting problem, which convex, for various regularizations constraints imposed generating function. We prove existence uniqueness result our problem provide estimate terms Wasserstein metric input measure. Then formulate discretization implemented numerically using available software packages analyze its approximation error. Finally, present empirical examples CRSP data from U.S. stock market, including performance allowing dividends, defaults, transaction costs.