发表机构
Hebrew University of Jerusalem（希伯来大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对离散分数布朗运动模型下的高频交易，采用平稳高斯序列谱方法推导最优确定性等价渐近增长率，证明经缩放的最优头寸收敛于高斯白噪声型场，为高频交易效用最大化提供理论支撑。
AI 中文摘要
我们研究离散分数布朗运动模型中高频交易的指数效用最大化问题，采用平稳高斯序列的谱方法推导最优确定性等价的渐近增长率，还证明经适当缩放的最优头寸在有限维分布下收敛于高斯白噪声型场。
英文摘要
We study utility maximization for high-frequency trading in fractional Brownian motion models. We first consider exponential utility in the discretized arithmetic model. Using spectral methods for stationary Gaussian sequences, we derive the asymptotic growth rate of the optimal certainty equivalent and the scaling limit of the optimal positions. We then consider power and logarithmic utility in a positive-price model with positive wealth and investment fractions in $[0,1]$. In this case, the logarithm of the optimal certainty equivalent grows at rate $n^{1-H}$ for $H\neq1/2$, with a coefficient determined by the one-sided prediction error of fractional Gaussian noise. We also give a simple binary strategy which attains this leading rate, without claiming exact finite-horizon optimality.
