随机波动率与交易成本下的投资组合选择
文章 arXiv papers · 作者: Dong Yan et al.
总结
本文研究资产波动率具有两个随机因子时的最优投资组合选择：一个均值回归成分和一个随机均值回归水平。交易会产生比例型外生成本，以及与随机流动性风险过程相关的内生成本。投资者偏好通过基于期权隐含信息的方法推导出的S形效用函数表示，并使用凹包变换处理其非凹性。
变换后的问题表示为五维非线性哈密顿—雅可比—贝尔曼方程。作者使用基于深度学习的策略迭代计算价值函数和最优投资策略，随后开展数值实验，考察交易成本和随机波动率如何影响投资选择。摘要描述了建模与计算方法，但未给出具体策略发现、市场校准或实证验证，因此结论仅限于既定模型下的数值分析。
核心观点
- 波动率模型包含均值回归因子和随机均值回归水平。
- 该框架结合比例型交易成本与流动性驱动的内生成本。
- 期权隐含的S形效用函数通过其凹包进行变换。
- 深度学习策略迭代方法以数值方式求解由此产生的非线性HJB问题。
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# Portfolio selection with exogenous and endogenous transaction costs under a two-factor stochastic volatility model # Portfolio selection with exogenous and endogenous transaction costs under a two-factor stochastic volatility model In this paper, we investigate a portfolio selection problem with transaction costs under a two-factor stochastic volatility structure, where volatility follows a mean-reverting process with a stochastic mean-reversion level. The model incorporates both proportional exogenous transaction costs and endogenous costs modeled by a stochastic liquidity risk process. Using an option-implied approach, we extract an S-shaped utility function that reflects investor behavior and apply its concave envelope transformation to handle the non-concavity. The resulting problem reduces to solving a five-dimensional nonlinear Hamilton-Jacobi-Bellman equation. We employ a deep learning-based policy iteration scheme to numerically compute the value function and the optimal policy. Numerical experiments are conducted to analyze how both types of transaction costs and stochastic volatility affect optimal investment decisions.
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