Applied Math Colloquium: Dr Maxim Bichuch

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.