Abstract
We propose an implementable, feedforward neural network-based structure preserving probabilistic numerical approximation for a generalized obstacle problem describing the value of a zero-sum differential game of optimal stopping with asymmetric information.
The target solution depends on three variables: the time, the spatial (or state) variable, and a variable from a standard $(I-1)$-simplex which represents the probabilities with which the $I$ possible configurations of the game are played.
The proposed numerical approximation preserves the convexity of the continuous solution as well as the lower and upper obstacle bounds.
We show convergence of the fully-discrete scheme to the unique viscosity solution of the continuous problem and present a range of numerical studies to demonstrate its applicability.
The target solution depends on three variables: the time, the spatial (or state) variable, and a variable from a standard $(I-1)$-simplex which represents the probabilities with which the $I$ possible configurations of the game are played.
The proposed numerical approximation preserves the convexity of the continuous solution as well as the lower and upper obstacle bounds.
We show convergence of the fully-discrete scheme to the unique viscosity solution of the continuous problem and present a range of numerical studies to demonstrate its applicability.
| Original language | English |
|---|---|
| Number of pages | 24 |
| Journal | arxiv : oa repository of preprints |
| DOIs | |
| Publication status | Submitted - 5 Dec 2023 |
Keywords
- Zero-sum game of optimal stopping-time
- Asymmetric information
- Probabilistic numerical approximation
- Discrete convex envelope
- Convexity constrained Hamilton–Jacobi–Bellmann equation
- Viscosity solution
- Feedforward Neural Network