Probability seminar by Giorgio Ferrari
Giorgio Ferrari gives a talk on probability theory. The talk is titled “On the Optimal Boundary of a Three-Dimensional Singular Stochastic Control Problem Arising in Irreversible Investment”.
Place: Hilbertrummet, ASA building, Åbo Akademi University, Turku, Finland.
Time: 28 January 2015, 3 PM.
Giorgio Ferrari is a post doctoral researcher at the Center for Mathematical Economics, Bielefeld University, Germany.
In this talk we examine 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.