A Stochastic Reversible Investment Problem on a Finite-Time Horizon: Free Boundary Analysis
A Stochastic Reversible Investment Problem on a Finite-Time Horizon: Free Boundary Analysis
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有限时间范围内的随机可逆投资问题：自由边界分析
DOI：
10.2139/ssrn.2289963
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
Giorgio Ferrari
中科院分区：
文献类型：
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作者：
T. de Angelis;Giorgio Ferrari
本文研究了在有摩擦的市场中，生产单一产品的企业的连续时间、有限时域、随机部分可逆投资问题。生产能力被建模为一个一维的，时间齐次的，线性扩散控制的有界变差过程，代表的累积投资-撤资策略。我们将投资-撤资问题与一个零和最优停止博弈相关联，并通过一个具有两个移动边界的自由边界问题来刻画其价值函数。这些是连续的、有界的和单调的曲线，其解决了沃尔泰拉型的非线性积分方程系统。最优的投资-撤资策略，然后被证明是一个扩散反映在两个边界。
We study a continuous-time, finite horizon, stochastic partially reversible investment problem for a firm producing a single good in a market with frictions. The production capacity is modeled as a one-dimensional, time-homogeneous, linear diffusion controlled by a bounded variation process which represents the cumulative investment–disinvestment strategy. We associate to the investment–disinvestment problem a zero-sum optimal stopping game and characterize its value function through a free-boundary problem with two moving boundaries. These are continuous, bounded and monotone curves that solve a system of non-linear integral equations of Volterra type. The optimal investment–disinvestment strategy is then shown to be a diffusion reflected at the two boundaries.