Schuhmann, Patrick: On some Two-Dimensional Singular Stochastic Control Problems and their Free-Boundary Analysis. 2021
Inhalt
- Introduction
- An Optimal Dividend Problem with Capital Injections over a Finite Horizon This Section is already published in a joint work with Giorgio Ferrari, see FerrariSchuhmann.
- Problem Formulation
- The Main Result
- On the Proof of Theorem 2.6
- On a Representation of the Optimal Stopping Value Function
- Integrating the Optimal Stopping Value Function
- A Case Study with Discounted Constant Marginal Profits and Costs
- Conclusion
- Optimal Production under Regime SwitchingThis project started during a research visit at the University of Edmonton under the supervision of Abel Cadenillas.
- Problem Formulation
- The Singular Stochastic Control Case
- Verification Theorem
- Construction of the Solution
- Verification of the Solution
- Comparative Statics and Numerical Examples
- The Bounded-Velocity Control Case
- Verification Theorem
- Construction of the Solution
- Verification of the Solution
- Comparative Statics and Numerical Examples
- Comparison Between Different Models
- Comparison Between the Singular and the Bounded-Velocity Control Cases
- The Singular Stochastic Control Case: A Comparison with the Single Regime Case
- The Bounded-Velocity Control Case: A Comparison with the Single Regime Case
- Conclusion
- A Singular Stochastic Control Problem with Interconnected Dynamics This section is already published in two joint works with Giorgio Ferrari and Salvatore Federico, see FedericoFerrariSchuhmann19 and FedericoFerrariSchuhmann20.
- Problem Formulation
- The Related Dynkin Game and Preliminary Properties of the Free-Boundaries
- The Structure of the Value Function
- Further Properties of the Free-Boundaries
- A System of Equations for the Free-Boundaries
- A System of Differential Equations for the Free-Boundaries
- A Discussion on Theorem 4.30 and on the Optimal Control
- Conclusion
- Appendices
- Appendix Section 2
- Appendix Section 4