Optimal Boundary Surface for Irreversible Investment with Stochastic Costs

Tiziano De Angelis, Salvatore Federico () and Giorgio Ferrari ()

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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 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.

Date: 2014-06, Revised 2017-01
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Citations: View citations in EconPapers (23)

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Related works:
Working Paper: Optimal boundary surface for irreversible investment with stochastic costs (2015)
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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1406.4297

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