摘要翻译：
即使面对不断恶化和高度波动的需求，企业也经常投资于而不是抛弃老化的技术。为了研究这一现象，我们将企业利润流模型化为一个负漂移的布朗运动。在每个时间点，公司可以继续运营，也可以停止并退出项目。此外，有一个一次性的选择进行投资，提高了项目的利润率。利用随机分析，我们证明了最优策略总是存在的，并且最优策略具有三个阈值。投资前有投资和退出门槛，投资后有退出门槛。我们还对关于布朗运动的漂移和波动性的阈值进行了比较静力学分析。当投资的利润增长足够大时，我们发现了一个新的结果：投资临界值在波动性中降低。
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英文标题：
《Invest or Exit? Optimal Decisions in the Face of a Declining Profit
  Stream》
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作者：
H. Dharma Kwon
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最新提交年份：
2019
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分类信息：

一级分类：Mathematics        数学
二级分类：Optimization and Control        优化与控制
分类描述：Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学，线性规划，控制论，系统论，最优控制，博弈论
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一级分类：Economics        经济学
二级分类：General Economics        一般经济学
分类描述：General methodological, applied, and empirical contributions to economics.
对经济学的一般方法、应用和经验贡献。
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一级分类：Quantitative Finance        数量金融学
二级分类：Economics        经济学
分类描述：q-fin.EC is an alias for econ.GN. Economics, including micro and macro economics, international economics, theory of the firm, labor economics, and other economic topics outside finance
q-fin.ec是econ.gn的别名。经济学，包括微观和宏观经济学、国际经济学、企业理论、劳动经济学和其他金融以外的经济专题
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一级分类：Quantitative Finance        数量金融学
二级分类：Mathematical Finance        数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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英文摘要：
  Even in the face of deteriorating and highly volatile demand, firms often invest in, rather than discard, aging technologies. In order to study this phenomenon, we model the firm's profit stream as a Brownian motion with negative drift. At each point in time, the firm can continue operations, or it can stop and exit the project. In addition, there is a one-time option to make an investment which boosts the project's profit rate. Using stochastic analysis, we show that the optimal policy always exists and that it is characterized by three thresholds. There are investment and exit thresholds before investment, and there is a threshold for exit after investment. We also effect a comparative statics analysis of the thresholds with respect to the drift and the volatility of the Brownian motion. When the profit boost upon investment is sufficiently large, we find a novel result: the investment threshold decreases in volatility.
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PDF链接：
https://arxiv.org/pdf/1901.01486