Applied Math Colloquium: Dr Maxim Bichuch
Johns Hopkins University
Title: Optimal Investment with Correlated Stochastic Volatility Factors
Abstract: The problem of portfolio allocation in the context of stocks evolving in random environments, that is
with volatility and returns depending on random factors, has attracted a lot of attention. The problem
of maximizing a power utility at a terminal time with only one random factor can be linearized thanks to
a classical distortion transformation. In the present paper, we address the problem with several factors
using a perturbation technique around the case where these factors are perfectly correlated reducing the
problem to the case with a single factor. We illustrate our result with a particular model for which we
have explicit formulas. A rigorous accuracy result is also derived using sub- and super-solutions of the
HJB equation involved. In order to keep the notations as explicit as possible, we treat the case with one
stock and two factors and we describe an extension to the case with two stocks and two factors.