High-Frequency Exponential-Utility Maximization under Fractional Brownian Motion

2026-08-05

AI Summary

This study addresses the problem of exponential utility maximization in high-frequency trading under fractional Brownian motion. By discretizing fractional Brownian motion into a stationary Gaussian sequence, the authors introduce a spectral method—applied for the first time in this context—to analyze the optimization problem. Combining this approach with limit theory for stochastic processes, they derive the asymptotic growth rate of the optimal certainty equivalent and establish that, after appropriate rescaling, the optimal position process converges in finite-dimensional distributions to a Gaussian white noise field. This work extends portfolio optimization theory to settings driven by fractional noise and reveals a universal structure underlying optimal strategies in the high-frequency limit.

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.

Problem

• exponential-utility maximization
• high-frequency trading
• fractional Brownian motion
• certainty equivalent
• optimal positions

Innovation

• fractional Brownian motion
• exponential utility maximization
• spectral methods
• high-frequency trading
• Gaussian white-noise field