On the Optimal Boundary of a Three-Dimensional Singular Stochastic Control Problem Arising in Irreversible Investment

Tiziano de Angelis, Salvatore Federico () and Giorgio Ferrari ()
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Tiziano de Angelis: Center for Mathematical Economics, Bielefeld University

No 509, Center for Mathematical Economics Working Papers from Center for Mathematical Economics, Bielefeld University

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.

Keywords: irreversible investment; singular stochastic control; optimal stopping; freeboundary problems; nonlinear integral equations (search for similar items in EconPapers)
Pages: 41
Date: 2016-03-14
New Economics Papers: this item is included in nep-ore
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Citations: View citations in EconPapers (2)

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