离散时间投资组合优化中的跳跃重要吗?

IF 3.7 4区 管理学 Q2 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Operations Research Perspectives Pub Date : 2024-07-29 DOI:10.1016/j.orp.2024.100312
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引用次数: 0

摘要

本文研究的是离散时间投资组合优化问题,其中标的风险资产遵循 Lévy GARCH 模型。除了高斯噪声,该框架还允许各种跳跃增量,包括无限活动跳跃。利用动态编程方法和模型的仿射性质,我们推导出了最优策略所满足的单一方程,并用数值证明了该方程在所有特殊情况下都有唯一解。在数值研究中,我们重点关注了跳跃的影响,并评估了采用无跳跃高斯 HN-GARCH 模型或同调变体的投资者的差异。我们发现,当根据跳跃模型的模拟收益进行重新校准时,这两种无跳跃模型都会产生微不足道的财富等值损失值。低财富等值损失值与跳跃模型中的修正参数保持一致,表明市场处于极端情况。因此,我们得出结论,更简单的模型可以成功地模仿离散时间条件异方差跳跃模型的策略和表现,从而支持从业人员的偏好。
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Do jumps matter in discrete-time portfolio optimization?

This paper studies a discrete-time portfolio optimization problem, wherein the underlying risky asset follows a Lévy GARCH model. Besides a Gaussian noise, the framework allows for various jump increments, including infinite-activity jumps. Using a dynamic programming approach and exploiting the affine nature of the model, we derive a single equation satisfied by the optimal strategy, and we show numerically that this equation leads to a unique solution in all special cases. In our numerical study, we focus on the impact of jumps and evaluate the difference to investors employing a Gaussian HN-GARCH model without jumps or a homoscedastic variant. We find that both jump-free models yield insignificant values for the wealth-equivalent loss when re-calibrated to simulated returns from the jump models. The low wealth-equivalent loss values remain consistent for modified parameters in the jump models, indicating extreme market situations. We therefore conclude, in support of practitioners’ preferences, that simpler models can successfully mimic the strategy and performance of discrete-time conditional heteroscedastic jump models.

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来源期刊
Operations Research Perspectives
Operations Research Perspectives Mathematics-Statistics and Probability
CiteScore
6.40
自引率
0.00%
发文量
36
审稿时长
27 days
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