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

de Angelis T, Federico S, Ferrari G (2014) Center for Mathematical Economics Working Papers; 509.
Bielefeld: Center for Mathematical Economics.

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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.
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de Angelis T, Federico S, Ferrari G. On the Optimal Boundary of a Three-Dimensional Singular Stochastic Control Problem Arising in Irreversible Investment. Center for Mathematical Economics Working Papers. Vol 509. Bielefeld: Center for Mathematical Economics; 2014.
de Angelis, T., Federico, S., & Ferrari, G. (2014). On the Optimal Boundary of a Three-Dimensional Singular Stochastic Control Problem Arising in Irreversible Investment (Center for Mathematical Economics Working Papers, 509). Bielefeld: Center for Mathematical Economics.
de Angelis, T., Federico, S., and Ferrari, G. (2014). On the Optimal Boundary of a Three-Dimensional Singular Stochastic Control Problem Arising in Irreversible Investment. Center for Mathematical Economics Working Papers, 509, Bielefeld: Center for Mathematical Economics.
de Angelis, T., Federico, S., & Ferrari, G., 2014. On the Optimal Boundary of a Three-Dimensional Singular Stochastic Control Problem Arising in Irreversible Investment, Center for Mathematical Economics Working Papers, no.509, Bielefeld: Center for Mathematical Economics.
T. de Angelis, S. Federico, and G. Ferrari, On the Optimal Boundary of a Three-Dimensional Singular Stochastic Control Problem Arising in Irreversible Investment, Center for Mathematical Economics Working Papers, vol. 509, Bielefeld: Center for Mathematical Economics, 2014.
de Angelis, T., Federico, S., Ferrari, G.: On the Optimal Boundary of a Three-Dimensional Singular Stochastic Control Problem Arising in Irreversible Investment. Center for Mathematical Economics Working Papers, 509. Center for Mathematical Economics, Bielefeld (2014).
de Angelis, Tiziano, Federico, Salvatore, and Ferrari, Giorgio. On the Optimal Boundary of a Three-Dimensional Singular Stochastic Control Problem Arising in Irreversible Investment. Bielefeld: Center for Mathematical Economics, 2014. Center for Mathematical Economics Working Papers. 509.
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