Optimal Boundary Surface for Irreversible Investment with Stochastic Costs
Optimal Boundary Surface for Irreversible Investment with Stochastic Costs
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DOI：
10.1287/moor.2016.0841
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发表时间：
2014-06
期刊：
影响因子：
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通讯作者：
T. Angelis;S. Federico;Giorgio Ferrari
中科院分区：
文献类型：
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作者：
T. Angelis;S. Federico;Giorgio Ferrari
本文研究了以生产总预期成本最小为目标的企业最优不可逆投资问题的马尔可夫模型。我们将市场不确定性和单位生产能力的投资成本建模为两个独立的一维规则扩散，并考虑了一个一般的凸运行成本函数。该优化问题被设置为一个三维退化奇异随机控制问题。我们给出了最优控制作为在适当的边界面上的反射扩散的解。这种边界源于对一类二维参数相关的最优停止问题的分析，其特征在于参数相关的Fredholm型非线性积分方程族的唯一连续解。
This paper examines a Markovian model for the optimal irreversible investment problem of a firm aiming at minimizing total expected costs of production. We model market uncertainty and the cost of investment per unit of production capacity, as two independent one-dimensional regular diffusions, and we consider a general convex running cost function. The optimization problem is set as a three-dimensional degenerate singular stochastic control problem. We provide the optimal control as the solution of a reflected diffusion at a suitable boundary surface. Such boundary arises from the analysis of a family of two-dimensional parameter-dependent optimal stopping problems, and it is characterized in terms of the family of unique continuous solutions to parameter-dependent, nonlinear integral equations of Fredholm type.