Downside risk optimization with random targets and portfolio amplitude
研究了在投资组合选择中最小化下行风险的优化问题，推导出针对常数目标和随机目标的最优投资组合显式解，并引入投资组合振幅这一新指标来刻画优化过程，解释了投资者为何偏好持有某些资产以追随随机目标。
In this paper, we discuss downside risk optimization in the context of portfolio selection. We derive explicit solutions to the optimal portfolios that minimize the downside risk with respect to constant targets and random targets. In doing so, we propose using portfolio amplitude, a new measure in the literature, to characterize the portfolio selection under the downside risk optimization. Particularly, we demonstrate a mechanism by which the random target inputs its impact into the system and alters the optimal solution. Our results underpin why investors prefer holding some specific assets in following random targets and provide explanations for some special investment strategies, such as constructing a stock portfolio following a bond index. We present numerical examples of stock portfolio management to support our theoretical results.