投资中期望利润和成本收益的最优停止 在不确定的情况下

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摘要翻译：
本文研究了不确定条件下投资的期望利润与成本现金流之间的权衡策略的有限时域最优停止问题。最优问题首先用一个相互阻碍的利润和成本收益的Snell包络系统来表示。然后，我们利用反射后向SDES相关系统的近似格式构造了极小和极大解。当现金流对不确定源（如市场价格波动）的依赖关系被假定为按扩散过程演化时，我们还得到了这些解与具有相互联系障碍的变分不等式(VI)系统的粘性解之间的联系。我们还提供了两个反例，说明(VI)解的唯一性一般不成立。
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英文标题：
《Optimal stopping of expected profit and cost yields in an investment
  under uncertainty》
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作者：
Boualem Djehiche (KTH Stockolm), Said Hamad\`ene (LMM), Marie Am\'elie
  Morlais (LMM)
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最新提交年份：
2010
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Portfolio Management        项目组合管理
分类描述：Security selection and optimization, capital allocation, investment strategies and performance measurement
证券选择与优化、资本配置、投资策略与绩效评价
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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：Mathematics        数学
二级分类：Probability        概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
--

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英文摘要：
  We consider a finite horizon optimal stopping problem related to trade-off strategies between expected profit and cost cash-flows of an investment under uncertainty. The optimal problem is first formulated in terms of a system of Snell envelopes for the profit and cost yields which act as obstacles to each other. We then construct both a minimal and a maximal solutions using an approximation scheme of the associated system of reflected backward SDEs. When the dependence of the cash-flows on the sources of uncertainty, such as fluctuation market prices, assumed to evolve according to a diffusion process, is made explicit, we also obtain a connection between these solutions and viscosity solutions of a system of variational inequalities (VI) with interconnected obstacles. We also provide two counter-examples showing that uniqueness of solutions of (VI) does not hold in general.
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PDF链接：
https://arxiv.org/pdf/1001.3289

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关键词：成本收益 不确定 Optimization Quantitative Differential Snell 最优 收益 假定 stopping