We consider risk‐averse investors with different levels of anxiety about asset price drawdowns. The latter is defined as the distance of the current price away from its best performance since inception. These drawdowns can increase either continuously or by jumps, and will contribute toward the investor's overall impatience when breaching the investor's private tolerance level. We investigate the unusual reactions of investors when aiming to sell an asset under such adverse market conditions. Mathematically, we study the optimal stopping of the utility of an asset sale with a random discounting that captures the investor's overall impatience. The random discounting is given by the cumulative amount of time spent by the drawdowns in an undesirable high region, fine‐tuned by the investor's personal tolerance and anxiety about drawdowns. We prove that in addition to the traditional take‐profit sales, the real‐life employed stop‐loss orders and trailing stops may become part of the optimal selling strategy, depending on different personal characteristics. This paper thus provides insights on the effect of anxiety and its distinction with traditional risk aversion on decision making.

中文翻译：

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何时因资产缩水而出售资产

我们考虑对资产价格下跌有不同程度焦虑的规避风险的投资者。后者定义为当前价格与自成立以来最佳表现的距离。这些亏损可以连续增加或跳跃增加，并且在超出投资者的私人承受能力水平时，会加剧投资者的整体耐心。我们打算在如此不利的市场条件下出售资产时，调查投资者的不同寻常反应。在数学上，我们研究了通过随机贴现来捕获投资者总体上的不耐烦情绪的资产出售效用的最优止损。随机折现是由不期望的高位区域的缩编所花费的累计时间得出的，并由投资者 对缩编的个人宽容和焦虑。我们证明，除了传统的获利销售外，实际生活中使用的止损订单和追踪止损可能会成为最佳销售策略的一部分，具体取决于不同的个人特征。因此，本文提供了有关焦虑影响及其与传统风险规避对决策的区别的见解。