Optimal boundary surface for irreversible investment with stochastic costs

Tiziano De Angelis (), Salvatore Federico () and Giorgio Ferrari ()
Additional contact information
Tiziano De Angelis: School of Mathematics, University of Leeds, Woodhouse Lane, Leeds LS2 9JT, United Kingdom
Giorgio Ferrari: Center for Mathematical Economics (IMW), Bielefeld University, Universitatsstrasse 25, D-33615 Bielefeld, Germany

No 2015-03, Working Papers - Mathematical Economics from Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa

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; freeboundary problems; nonlinear integral equations. (search for similar items in EconPapers)
JEL-codes: C02 C73 D92 E22 (search for similar items in EconPapers)
Pages: 39 pages
Date: 2015-10
New Economics Papers: this item is included in nep-mac and nep-ore
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Citations: View citations in EconPapers (2)

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Related works:
Working Paper: Optimal Boundary Surface for Irreversible Investment with Stochastic Costs (2017)
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