Optimal Boundary Surface for Irreversible Investment with Stochastic   Costs
  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. 
Tiziano De Angelis, Salvatore Federico and Giorgio Ferrari
math.PR math.OC q-fin.MF