Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/103927
Authors: 
De Angelis, Tiziano
Federico, Salvatore
Ferrari, Giorgio
Year of Publication: 
2014
Series/Report no.: 
Working Papers, Center for Mathematical Economics 509
Abstract: 
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 free-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.
Subjects: 
irreversible investment
singular stochastic control
optimal stopping
free-boundary problems
nonlinear integral equations
JEL: 
C02
C73
E22
D92
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

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