英文标题：
《Irreversible Investment under L\\\'evy Uncertainty: an Equation for the
Optimal Boundary》
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作者：
Giorgio Ferrari, Paavo Salminen
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最新提交年份：
2014
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英文摘要：
We derive a new equation for the optimal investment boundary of a general irreversible investment problem under exponential L\\\'evy uncertainty. The problem is set as an infinite time-horizon, two-dimensional degenerate singular stochastic control problem. In line with the results recently obtained in a diffusive setting, we show that the optimal boundary is intimately linked to the unique optional solution of an appropriate Bank-El Karoui representation problem. Such a relation and the Wiener Hopf factorization allow us to derive an integral equation for the optimal investment boundary. In case the underlying L\\\'evy process hits any real point with positive probability we show that the integral equation for the investment boundary is uniquely satisfied by the unique solution of another equation which is easier to handle. As a remarkable by-product we prove the continuity of the optimal investment boundary. The paper is concluded with explicit results for profit functions of (i) Cobb-Douglas type and (ii) CES type. In the first case the function is separable and in the second case non-separable.
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中文摘要：
我们推导了一个新的方程，用于在指数Léevy不确定性下一般不可逆投资问题的最优投资边界。该问题被设置为一个无限时域二维退化奇异随机控制问题。与最近在扩散环境中获得的结果一致，我们证明了最优边界与适当的Bank-El-Karoui表示问题的唯一可选解密切相关。这种关系和Wiener-Hopf分解使我们能够导出最优投资边界的积分方程。如果潜在的LSevy过程以正概率击中任何实点，我们证明投资边界的积分方程由另一个更容易处理的方程的唯一解唯一满足。作为一个显著的副产品，我们证明了最优投资边界的连续性。本文最后给出了（i）Cobb-Douglas型和（ii）CES型利润函数的显式结果。在第一种情况下，函数是可分离的，在第二种情况下，函数是不可分离的。
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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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