High-Frequency Exponential-Utility Maximization under Fractional Brownian Motion

Abstract

We study exponential-utility maximization for high-frequency trading in a discretized fractional Brownian motion model. Using spectral methods for stationary Gaussian sequences, we derive the asymptotic growth rate of the optimal certainty equivalent. We also show that the suitably rescaled optimal positions converge in finite-dimensional distributions to a Gaussian white-noise-type field.