论文标题
在不可逆转的投资练习边界上的统一观点，在随机，均匀的容量扩张问题中
A unifying view on the irreversible investment exercise boundary in a stochastic, time-inhomogeneous capacity expansion problem
论文作者
论文摘要
本文设计了一种应用银行和El Karoui代表定理的方法，以找到丰富的随机，连续的时间容量扩展问题的投资边界，尽管存在有限的时间间隔$ [0，t] $，尽管存在与终端时间$ t $ t $相关的国家依赖废料值。对于提出的奇异随机控制问题而言，标准变分方法是不可行的，但是它承认了一些一阶条件，但是通过涉及废料值函数的额外的非积分项并取决于初始容量$ y $，这使得通过制定一种应用代表定理来解决。这样的设计，新的和感兴趣的本身，提供了基本容量$ l^{\ star} _y（t）$的存在，这是一个正面的积极级别，最佳投资过程被证明是活跃的。据我们所知，从未在此范围内应用代表定理。在确定性系数的特殊情况下，根据废料价值案例的进一步假设，对投资最佳的曲线的统一观点：基本容量等于通过变量方法获得的投资边界$ {\ hat y}（t）$。
This paper devises a way to apply the Bank and El Karoui Representation Theorem to find the investment boundary of a rich stochastic, continuous time capacity expansion problem with irreversible investment on the finite time interval $[0, T]$, despite the presence of a state dependent scrap value associated with the production facility at the terminal time $T$. Standard variational methods are not feasible for the proposed singular stochastic control problem but it admits some first order conditions, complicated however by an extra, non integral term involving the scrap value function and depending on the initial capacity $y$, which are solved by devising a way to apply the Representation Theorem. Such devise, new and of interest in its own right, provides the existence of the base capacity $l^{\star}_y(t)$, a positive level which the optimal investment process is shown to become active at. As far as we know the Representation Theorem has never been applied to this extent. In the special case of deterministic coefficients, under a further assumption specific to the scrap value case, a unifying view on the curve at which it is optimal to invest emerges: the base capacity equals the investment boundary ${\hat y}(t)$ obtained by variational methods.
