标题： 具有瞬时和持续价格影响、可预测收益和多尺度随机波动性的最优交易 显示英文标题

标题： Optimal Trading under Instantaneous and Persistent Price Impact, Predictable Returns and Multiscale Stochastic Volatility

摘要： 我们考虑一个动态投资组合优化问题，该问题结合了可预测收益、瞬时交易成本、价格影响和随机波动率，扩展了Garleanu和Pedersen（2013）的经典结果，后者假设波动率是恒定的。 在这一一般情况下构建最优投资组合策略具有挑战性，因为由此产生的哈密顿-雅可比-贝尔曼（HJB）方程具有非线性特性。 为了解决这个问题，我们提出了一种多尺度波动率展开方法，该方法捕捉不同时间尺度上的随机波动率动态。 具体而言，分析涉及对快速均值回归波动率因子的奇异摄动和对缓慢移动因子的常规摄动。 我们还引入了一个小价格影响的近似，并证明了其数值准确性。 我们正式推导了二阶的渐近近似，并使用蒙特卡洛模拟展示了如何通过包含这些修正来提高所得投资组合策略的损益（PnL）。 显示英文摘要

摘要： We consider a dynamic portfolio optimization problem that incorporates predictable returns, instantaneous transaction costs, price impact, and stochastic volatility, extending the classical results of Garleanu and Pedersen (2013), which assume constant volatility. Constructing the optimal portfolio strategy in this general setting is challenging due to the nonlinear nature of the resulting Hamilton-Jacobi-Bellman (HJB) equations. To address this, we propose a multi-scale volatility expansion that captures stochastic volatility dynamics across different time scales. Specifically, the analysis involves a singular perturbation for the fast mean-reverting volatility factor and a regular perturbation for the slow-moving factor. We also introduce an approximation for small price impact and demonstrate its numerical accuracy. We formally derive asymptotic approximations up to second order and use Monte Carlo simulations to show how incorporating these corrections improves the Profit and Loss (PnL) of the resulting portfolio strategy.