Long-Only Robust Asymptotic Growth in Stochastic Portfolio Theory

We consider the problem of maximizing the asymptotic growth rate of an investor under drift uncertainty in the setting of stochastic portfolio theory (SPT). Following the work of Kardaras and Robertson [Ann. Appl. Probab., Forthcoming] we take as inputs (i) a Markovian volatility matrix c(x) and (ii) an invariant density p(x) for the market weights, but we additionally impose long-only constraints on the investor. Our principal contribution is proving a uniqueness and existence result for the class of concave functionally generated portfolios and developing a finite dimensional approximation, which can be used to numerically find the optimum.

We will also discuss extensions of the class of models obtained from the inputs (c,p). In particular we extend the construction to accommodate rank-based models and show that two of the main classes of models in SPT -- volatility-stabilized and Atlas models -- are of this type.

This is joint work with Martin Larsson.

Bio: David Itkin grew up in Canada and obtained his undergraduate degree in 2017 from the University of Western Ontario in mathematics and financial modelling. He is currently a 4th year PhD student in the Mathematical Sciences department at Carnegie Mellon University working with Martin Larsson. His research interests include stochastic portfolio theory and ergodic theory for diffusions.