HN-GARCH模型下时间一致的均值方差投资组合*

doi:10.7523/j.ucas.2025.002

中国科学院大学学报

HN-GARCH模型下时间一致的均值方差投资组合^*

阮中杰¹, 罗翠翠^2†

¹中国科学院大学数学科学学院,北京 100049;
²中国科学院大学国际学院,北京 100190

收稿日期:2024-10-15 修回日期:2025-01-10
通讯作者: ^†E-mail：luocuicui@ucas.ac.cn
基金资助:
^*国家自然科学基金（72210107001）、北京市自然科学基金（IS23128）、中央高校基本科研业务费和中国科学院PIFI国际杰出团队项目（2024PG0013）资助

Time-consistent mean-variance portfolio selection under HN-GARCH

RUAN Zhongjie¹, LUO Cuicui²

¹School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China;
²International College, University of Chinese Academy of Sciences, Beijing 100190, China

Received:2024-10-15 Revised:2025-01-10

摘要/Abstract

摘要： 本文在HN-GARCH模型下推导出均值-方差投资组合问题时间一致的均衡解。然后,以指数效用下的最优解作为参照,本文引入一个评价资产组合表现的指标,即“确定性等价回报损失”（certainty equivalent return loss, CErL）。最后,基于纳斯达克100股指的历史数据,蒙特卡洛模拟表明 GARCH 模型下的时间一致的资产组合在 CErL和夏普率的表现上优于同方差模型下的表现,非对称型GARCH模型的表现优于对称型GARCH。

关键词: HN-GARCH模型, 均值-方差, 时间一致, 指数效用, 确定性等价回报损失

Abstract: In this paper, we derive a time-consistent solution for mean-variance portfolio selection within the framework of the HN-GARCH model. Then, by using the optimal solution derived under exponential utility as a reference point, we introduce a well-defined performance metric, namely certainty equivalent return loss (certainty equivalent return loss, CErL), to assess portfolio performance. Finally, based on the historical data of the NASDAQ-100 Index, Monte Carlo simulation empirically demonstrate that the solution under the GARCH model outperforms that under a homoscedastic variant in terms of CErL and the performance of asymmetric GARCH is better than symmetric GARCH’s performance.

Key words: HN-GARCH model, mean-variance, time-consistent, exponential utility, certainty equivalent return loss

中图分类号:

O221.5

阮中杰, 罗翠翠. HN-GARCH模型下时间一致的均值方差投资组合^*[J]. 中国科学院大学学报, DOI: 10.7523/j.ucas.2025.002.

RUAN Zhongjie, LUO Cuicui. Time-consistent mean-variance portfolio selection under HN-GARCH[J]. Journal of University of Chinese Academy of Sciences, DOI: 10.7523/j.ucas.2025.002.

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