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Dianetti, Jodi; Ferrari, Giorgio: Multidimensional Singular Control and Related Skorokhod Problem: Suficient Conditions for the Characterization of Optimal Controls. In: . Vol.645. 2021, page 38 et seq.
Content
1. Introduction
1.1. Notation
2. Problem formulation and main result
2.1. Singular control and Skorokhod problem
2.2. Assumptions and main result
3. Proof of Theorem 2.5 for constant volatility
3.1. Step a: A connection to Dynkin games and the monotonicity property
3.2. Step b: Construction of -optimal policies
3.3. Step c: Characterization of the optimal control
4. On the proof of Theorem 2.5 for linear volatility
4.1. A preliminary lemma
4.2. Sketch of the proof of Theorem 2.5
5. Comments, extensions and examples
5.1. Refinements of Assumption 2.1
5.2. Some remarks
5.3. Examples
5.4. An example with degenerate dynamics
Appendix A. On the HJB equation
Appendix B. Proof of Lemma 2.3 and of Proposition 3.10
B.1. Proof of Lemma 2.3
B.2. Proof of Proposition 3.10
References