| Funding: | German Research Foundation (DFG) via grant RI 1128-4-4-1 and RI 1128-4-4-2 |
| Members: | Frank RIEDEL, Giorgio FERRARI, Jan-Henrik STEG |
| Duration: |
RI 1128-4-4-1: 2012 - 2015 RI 1128-4-4-2: 2015 - 2017 |
Strategic decisions of firms often have to be made under uncertainty and moreover imply long-ranging consequences, for example if they are hardly reversible due to physical or legal frictions. In this project we address these aspects with new methods. On the one hand we apply the most recent findings concerning model uncertainty ("Knightian Ambiguity") to such decisions. On the other hand we develop a theory of dynamic oligopoly games with irreversible capacity choices in continuous time. For such games, there exists no satisfying game theory, since a mathematically consistent game theoretic equilibrium concept (which allows for feedback) has not been successfully established so far. We use a new method for solving singular control problems, which has been (co-)developed by the principle investigator, to establish such a game theory. We will analyse in particular oligopoly games under Knightian uncertainty. For instance, we want to clarify the question whether the value of the option to wait disappears already with two firms.
(1) G. Ferrari, P. Salminen, Irreversible Investment under Lèvy Uncertainty: an Equation for the Optimal Boundary, forthcoming on Advances in Applied Probability. arXiv:1411.2395.
(2) M.B. Chiarolla, G. Ferrari, G. Stabile, Optimal Dynamic Procurement Policies for a Storable Commodity with Lèvy Prices and Convex Holding Costs, European Journal of Operational Research 247(3) (2015), pp. 847-858.
(3) T. De Angelis, G. Ferrari, J. Moriarty, A Non Convex Singular Stochastic Control Problem and its Related Optimal Stopping Boundaries, SIAM Journal on Control and Optimization 53(3) (2015), pp. 1199-1223.
(4) G. Ferrari, On an Integral Equation for the Free-Boundary of Stochastic, Irreversible Investment Problems, The Annals of Applied Probability 25(1) (2015), pp. 150-176.
(5) T. De Angelis, G. Ferrari, A Stochastic Partially Reversible Investment Problem on a Finite-Time Horizon: Free-Boundary Analysis, Stochastic Processes and their Applications 124(3) (2014), pp. 4080-4119.
(6) M.B. Chiarolla, G. Ferrari, Identifying the Free Boundary of a Stochastic, Irreversible Investment Problem via the Bank-El Karoui Representation Theorem, SIAM Journal on Control and Optimization 52(2) (2014), pp. 1048-1070.
(7) M.B. Chiarolla, G. Ferrari, F. Riedel, Generalized Kuhn-Tucker Conditions for N-Firm Stochastic Irreversible Investment under Limited Resources, SIAM Journal on Control and Optimization 51(5) (2013), pp. 3863-3885.
(1) T. De Angelis, G. Ferrari, J. Moriarty, Nash equilibria of threshold type for two-player nonzero-sum games of stopping, arXiv:1508.03989, 2015. Submitted.
(2) T. De Angelis, G. Ferrari, J. Moriarty, A solvable two-dimensional degenerate singular stochastic control problem with non convex costs, arXiv:1411.2428, 2015. Submitted.
(3) T. De Angelis, S. Federico, G. Ferrari, Optimal Boundary Surface for Irreversible Investment with Stochastic Costs, arXiv:1406.4297, 2015. Submitted.
(4) G. Ferrari, F. Riedel, J.H. Steg, Continuous-time Public Good Contribution under Uncertainty: a Stochastic Control Approach, arXiv:1307.2849, 2013. Submitted.