Rates of return (drifts) are notoriously hard to estimate. Yet optimal portfolio choice depends on them, which can lead to error-prone optimal portfolios. Kardaras and Robertson recently introduced an elegant approach to robust long-term growth rate maximization in a model where the volatility structure is Markovian and known, while drifts are unknown but constrained to be consistent with certain long-term average statistics of asset returns. Optimal strategies are computed by solving a high-dimensional PDE. We develop a rich parametric family of models for which explicit solutions are available in arbitrary dimension. This reveals that robust optimal strategies tend to include significant short selling, which may be undesirable or infeasible. We introduce risk constraints in the form of drawdown constraints, which does not affect tractability, and long-only constraints, which requires numerical solutions. Using tools from stochastic portfolio theory, we develop a numerical method for handling long-only constraints.

Martin Larsson is a Swedish mathematician working in mathematical finance. Larsson earned his doctorate from Cornell University in 2012, under the supervision of Robert Jarrow. He was a postdoctoral fellow at the Swiss Finance Institute at EPFL in Lausanne until 2014, and then an assistant professor at ETH Zurich until 2019. He is currently an associate professor at the Department of Mathematical Sciences at Carnegie Mellon University in Pittsburgh, US.