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Media type:
E-Article
Title:
Optimal Boundary Surface for Irreversible Investment with Stochastic Costs
Contributor:
De Angelis, Tiziano;
Federico, Salvatore;
Ferrari, Giorgio
imprint:
Institute for Operations Research and the Management Sciences, 2017
Published in:Mathematics of Operations Research
Language:
English
ISSN:
0364-765X;
1526-5471
Origination:
Footnote:
Description:
<p>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.</p>