Optimal Boundary Surface for Irreversible Investment with Stochastic Costs

De Angelis T, Federico S, Ferrari G (2017)
Mathematics of Operations Research 42(4): 1135-1161.

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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 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.
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De Angelis T, Federico S, Ferrari G. Optimal Boundary Surface for Irreversible Investment with Stochastic Costs. Mathematics of Operations Research. 2017;42(4):1135-1161.
De Angelis, T., Federico, S., & Ferrari, G. (2017). Optimal Boundary Surface for Irreversible Investment with Stochastic Costs. Mathematics of Operations Research, 42(4), 1135-1161. doi:10.1287/moor.2016.0841
De Angelis, T., Federico, S., and Ferrari, G. (2017). Optimal Boundary Surface for Irreversible Investment with Stochastic Costs. Mathematics of Operations Research 42, 1135-1161.
De Angelis, T., Federico, S., & Ferrari, G., 2017. Optimal Boundary Surface for Irreversible Investment with Stochastic Costs. Mathematics of Operations Research, 42(4), p 1135-1161.
T. De Angelis, S. Federico, and G. Ferrari, “Optimal Boundary Surface for Irreversible Investment with Stochastic Costs”, Mathematics of Operations Research, vol. 42, 2017, pp. 1135-1161.
De Angelis, T., Federico, S., Ferrari, G.: Optimal Boundary Surface for Irreversible Investment with Stochastic Costs. Mathematics of Operations Research. 42, 1135-1161 (2017).
De Angelis, Tiziano, Federico, Salvatore, and Ferrari, Giorgio. “Optimal Boundary Surface for Irreversible Investment with Stochastic Costs”. Mathematics of Operations Research 42.4 (2017): 1135-1161.
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