英文标题：
《Optimal Boundary Surface for Irreversible Investment with Stochastic
Costs》
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作者：
Tiziano De Angelis, Salvatore Federico and Giorgio Ferrari
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最新提交年份：
2017
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英文摘要：
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 Skorohod reflection problem 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.
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中文摘要：
本文研究了以生产总预期成本最小化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正则扩散，并考虑一个一般的凸运行成本函数。该优化问题是一个三维退化奇异随机控制问题。我们将最优控制作为Skorohod反射问题在合适的边界曲面上的解。这种边界源于对一类二维参数相关最优停止问题的分析，其特征是参数相关的Fredholm型非线性积分方程的唯一连续解族。
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分类信息：

一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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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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一级分类：Quantitative Finance 数量金融学
二级分类：Mathematical Finance 数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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