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摘要翻译：
我们研究了一个有限时域上生产单一商品的企业的随机连续时间模型。我们将生产能力建模为一个由表示累积投资的非递减过程控制的Ito扩散。企业的目标是通过选择最优的投资过程来最大化其预期的总净利润。这是一个奇异随机控制问题。我们根据Bank和El Karoui(2004)的思想，导出了最优性的一阶条件，并用基容量过程刻画了最优解，即表示问题的唯一解。当控制扩散系数是时间的确定性函数时，我们证明了基容量是确定性的，并用相应的最优停止问题的自由边界来辨识基容量。这在有限时域奇异随机控制问题的文献中是一个新的发现。作为子积，这一结果使我们可以得到自由边界的积分方程，我们在无限时域情况下显式地求解Cobb-Douglas生产函数和常系数的受控能力过程。
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英文标题：
《Identifying the Free Boundary of a Stochastic, Irreversible Investment
Problem via the Bank-El Karoui Representation Theorem》
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作者：
Maria B. Chiarolla, Giorgio Ferrari
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最新提交年份：
2013
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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：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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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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英文摘要：
We study a stochastic, continuous time model on a finite horizon for a firm that produces a single good. We model the production capacity as an Ito diffusion controlled by a nondecreasing process representing the cumulative investment. The firm aims to maximize its expected total net profit by choosing the optimal investment process. That is a singular stochastic control problem. We derive some first order conditions for optimality and we characterize the optimal solution in terms of the base capacity process, i.e. the unique solution of a representation problem in the spirit of Bank and El Karoui (2004). We show that the base capacity is deterministic and it is identified with the free boundary of the associated optimal stopping problem, when the coefficients of the controlled diffusion are deterministic functions of time. This is a novelty in the literature on finite horizon singular stochastic control problems. As a subproduct this result allows us to obtain an integral equation for the free boundary, which we explicitly solve in the infinite horizon case for a Cobb-Douglas production function and constant coefficients in the controlled capacity process.
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PDF链接：
https://arxiv.org/pdf/1108.4886
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