Optimal Boundary Surface for Irreversible Investment with Stochastic Costs

• 成果类型: Article
• 署名作者: De Angelis, Tiziano; Federico, Salvatore; Ferrari, Giorgio
• 署名单位: University of Leeds; University of Siena; University of Bielefeld
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2016.0841
• 发表日期: 2017
• 页码: 1135-1161
• 关键词: partially reversible investment; connections; continuity; time

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 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.