Optimal Boundary Surface for Irreversible Investment with Stochastic Costs

Tiziano De Angelis (), Salvatore Federico () and Giorgio Ferrari ()
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Tiziano De Angelis: School of Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom
Salvatore Federico: Dipartimento di Economia Politica e Statistica, Università degli Studi di Siena, 53100 Siena, Italy
Giorgio Ferrari: Center for Mathematical Economics (IMW), Bielefeld University, D-33615 Bielefeld, Germany

Mathematics of Operations Research, 2017, vol. 42, issue 4, 1135-1161

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 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.

Keywords: irreversible investment; singular stochastic control; optimal stopping; free-boundary problems; nonlinear integral equations (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (21)

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