Finite-time horizon, stopper vs. singular-controller games on the half-line
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866912448093618176 |
|---|---|
| author | Bovo, Andrea De Angelis, Tiziano |
| author_facet | Bovo, Andrea De Angelis, Tiziano |
| contents | We prove existence of a value for two-player zero-sum stopper vs. singular-controller games on finite-time horizon, when the underlying dynamics is one-dimensional, diffusive and bound to evolve in $[0,\infty)$. We show that the value is the maximal solution of a variational inequality with both obstacle and gradient constraint and satisfying a Dirichlet boundary condition at $[0,T)\times\{0\}$. Moreover, we obtain an optimal strategy for the stopper. In order to achieve our goals, we rely on new probabilistic methods, yielding gradient bounds and equi-continuity for the solutions of penalised partial differential equations that approximate the variational inequality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_06049 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Finite-time horizon, stopper vs. singular-controller games on the half-line Bovo, Andrea De Angelis, Tiziano Optimization and Control Analysis of PDEs Probability 91A05, 91A15, 60G40, 93E20, 49J40 We prove existence of a value for two-player zero-sum stopper vs. singular-controller games on finite-time horizon, when the underlying dynamics is one-dimensional, diffusive and bound to evolve in $[0,\infty)$. We show that the value is the maximal solution of a variational inequality with both obstacle and gradient constraint and satisfying a Dirichlet boundary condition at $[0,T)\times\{0\}$. Moreover, we obtain an optimal strategy for the stopper. In order to achieve our goals, we rely on new probabilistic methods, yielding gradient bounds and equi-continuity for the solutions of penalised partial differential equations that approximate the variational inequality. |
| title | Finite-time horizon, stopper vs. singular-controller games on the half-line |
| topic | Optimization and Control Analysis of PDEs Probability 91A05, 91A15, 60G40, 93E20, 49J40 |
| url | https://arxiv.org/abs/2409.06049 |