Dianetti, Jodi: Stochastic singular control: existence, characterization and approximation of solutions in cost minimization problems and games. 2022
Inhalt
- Introduction
- Chapter 2: Singular control and Skorokhod problem
- Chapter 3: Submodular N-player games with singular controls
- Chapter 4: Submodular mean field games with regular and singular controls
- Chapter 5: Stationary mean field games with singular control
- Outline of the thesis
- Singular control and related Skorokhod problem
- Problem formulation and main result
- Proof of Theorem 2.1.5 for constant volatility
- Step a: A connection to Dynkin games and the monotonicity property
- Step b: Construction of -optimal policies
- Step c: Characterization of the optimal control
- On the proof of Theorem 2.1.5 for linear volatility
- Comments, extensions and examples
- Auxiliary results: On the HJB equation
- Auxiliary results: Proof of Lemma 2.1.3 and of Proposition 2.2.10
- Submodular N-player games with singular controls
- The monotone-follower game
- Definition of the monotone-follower game
- Existence of Nash equilibria in the submodular monotone-follower game
- Some remarks
- The n-Lipschitz game
- Existence and approximation of weak Nash equilibria
- Weak formulation of the monotone-follower game.
- Assumptions and a preliminary lemma
- Existence and approximation of weak Nash equilibria
- On Lipschitz -Nash equilibria for the monotone-follower game
- Some remarks
- Applications and examples
- Submodular mean field games with regular and singular controls
- The submodular mean field game
- The mean field game problem
- The lattice structure
- The submodularity condition
- The best-response-map
- Existence and approximation of MFG solutions
- Remarks and examples
- Relaxed submodular mean field games
- Submodular mean field games with singular controls
- Concluding remarks and further extensions
- On the multidimensional case
- On linear-quadratic MFG
- On a geometric dynamics
- On mean field dependent dynamics
- On mean field games with common noise
- Stationary mean field games with singular controls
- The probabilistic setting
- The stationary mean field games
- Existence, uniqueness, and characterization of the mean field equilibria
- Connecting discounted and ergodic MFGs: The Abelian limit
- MFG vs. N-player games: approximation results
- On the Meyer-Zheng convergence
- Results on lattices of measures