We study a stochastic, continuous time model on a finite horizon for a firm that produces a single good. We model the production capacity as an Ito diffusion controlled by a nondecreasing process representing the cumulative investment. The firm aims to maximize its expected total net profit by choosing the optimal investment process. That is a singular stochastic control problem. We derive some first order conditions for optimality and we characterize the optimal solution in terms of the base capacity process, i.e. the unique solution of a representation problem in the spirit of Bank and El Karoui (2004). We show that the base capacity is deterministic and it is identified with the free boundary of the associated optimal stopping problem, when the coefficients of the controlled diffusion are deterministic functions of time. This is a novelty in the literature on finite horizon singular stochastic control problems. As a subproduct this result allows us to obtain an integral equation for the free boundary, which we explicitly solve in the infinite horizon case for a Cobb-Douglas production function and constant coefficients in the controlled capacity process.
Optimal Entry to an Irreversible Investment Plan with Non Convex Costs
最近在De Angelis，Ferrari和Moriarty（2015）[SIAM J. Control Optim. 53（3）]。这个问题可以被认为是一个不可逆的投资与成本功能，这是非凸的控制变量。在本文中，我们研究的最佳进入这个投资计划。最优进入策略可以有一个不规则的边界所产生的非凸性，与扭结的形状。
School of Management and Economics, ESOMAS, University of Turin（都灵大学管理经济学院）；Collegio Carlo Alberto（卡洛阿尔贝托学院）；Department of Modeling and Engineering Risk and Complexity, Scuola Superiore Meridionale（南方高等学院建模与工程风险与复杂性系）；CREST, ENSAE, Institute Polytechinique de Paris（巴黎理工学院ENSAE CREST研究中心）
