发表机构
School of Mathematical Sciences, Fudan University; FinTech Thrust, Hong Kong University of Science and Technology (Guangzhou)（复旦大学数学科学学院; 香港科技大学（广州）金融科技学域）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究在粗糙Hawkes--Heston模型中提出方差最优对冲方法，利用条件仿射变换和Galtchouk--Kunita--Watanabe投影获得半显式对冲，并通过核正则化与截断证明收敛性，数值实验验证了构造。
AI 中文摘要
我们研究了粗糙Hawkes--Heston模型中的方差最优股票对冲以及近似策略的收敛性。从该模型的条件仿射变换和仿射Volterra跳跃框架出发，我们获得了欧式看涨期权的半显式对冲，并通过Galtchouk--Kunita--Watanabe投影得到了最小二次误差的表示。我们的主要近似结果在保持原始股票、方差驱动因子和信息流不变的同时，对用于评估对冲的核进行正则化。为了处理奇异记忆和常见的标记跳跃，我们从交易前可用的历史信息构造近似持仓，并保持条件变换的随机模量包络。Riccati--Volterra稳定性和加权截断在紧致Fourier区间上产生了原始股票交易范数下的收敛性。对于看涨期权，核正则化和Fourier截断的联合选择给出了初始资本和策略的收敛性、连续时间收益的关于时间一致均方收敛性，以及终端均方误差向方差最优值的收敛性。一个带有平移分数核的数值实验在常见的原始市场路径上说明了该构造。
英文摘要
We study variance-optimal stock hedging and the convergence of approximate strategies in the rough Hawkes--Heston model. Starting from the model's affine conditional transform and the affine Volterra jump framework, we obtain semi-explicit hedges for European calls and a representation of the minimum quadratic error through the Galtchouk--Kunita--Watanabe projection. Our main approximation result keeps the original stock, variance driver, and information flow fixed while regularizing the kernel used to evaluate the hedge. To handle singular memory and common marked jumps, we construct the approximate holdings from histories available before trading and preserve the conditional transform's random modulus envelope. Riccati--Volterra stability and weighted truncation then yield convergence in the original stock's trading norm on compact Fourier intervals. For calls, a joint choice of kernel regularization and Fourier cutoff gives convergence of the initial capitals and strategies, uniform-in-time square-mean convergence of continuous-time gains, and convergence of the terminal mean-square error to the variance-optimal value. A numerical experiment with shifted fractional kernels illustrates the construction on common original-market paths.
