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arXiv · 1406.4297

Optimal Boundary Surface for Irreversible Investment with Stochastic Costs

Tiziano De Angelis·Salvatore Federico·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.

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BibTeXRIS

Tiziano De Angelis, Salvatore Federico, Giorgio Ferrari. 2014-06-17. Optimal Boundary Surface for Irreversible Investment with Stochastic Costs. https://arxiv.org/abs/1406.4297

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