摘要翻译：
本文研究了具有N个厂商的市场中资源有限的连续时间最优随机投资问题。投资过程受时间依赖的随机约束。我们不是用动态规划的方法，而是利用利润泛函的凹性导出了相应的社会规划者最优策略的一阶充要条件。我们的条件是Kuhn-Tucker定理的无限维随机推广。拉格朗日乘子的形式是在[0，t]上的一个非负可选随机测度，它与约束约束的时间集持平，即当所有燃料都耗尽时。作为子产物，我们得到了银行（2005）中单个企业的一阶条件的启发性解释。在无限时域情形下，当营业利润函数为Cobb-Douglas型时，我们的方法允许根据“基本能力”过程显式地计算最优策略，即Bank和El Karoui表示问题（2004）的唯一解。
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英文标题：
《Generalized Kuhn-Tucker Conditions for N-Firm Stochastic Irreversible
  Investment under Limited Resources》
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作者：
Maria B. Chiarolla, Giorgio Ferrari and Frank Riedel
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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：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：
  In this paper we study a continuous time, optimal stochastic investment problem under limited resources in a market with N firms. The investment processes are subject to a time-dependent stochastic constraint. Rather than using a dynamic programming approach, we exploit the concavity of the profit functional to derive some necessary and sufficient first order conditions for the corresponding Social Planner optimal policy. Our conditions are a stochastic infinite-dimensional generalization of the Kuhn-Tucker Theorem. The Lagrange multiplier takes the form of a nonnegative optional random measure on [0,T] which is flat off the set of times for which the constraint is binding, i.e. when all the fuel is spent. As a subproduct we obtain an enlightening interpretation of the first order conditions for a single firm in Bank (2005). In the infinite-horizon case, with operating profit functions of Cobb-Douglas type, our method allows the explicit calculation of the optimal policy in terms of the `base capacity' process, i.e. the unique solution of the Bank and El Karoui representation problem (2004).
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PDF链接：
https://arxiv.org/pdf/1203.3757