Numerical approximation of Dynkin games with asymmetric information
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866929687075225600 |
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| author | Baňas, Ľubomír Ferrari, Giorgio Randrianasolo, Tsiry Avisoa |
| author_facet | Baňas, Ľubomír Ferrari, Giorgio Randrianasolo, Tsiry Avisoa |
| contents | We propose an implementable, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_01847 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Numerical approximation of Dynkin games with asymmetric information Baňas, Ľubomír Ferrari, Giorgio Randrianasolo, Tsiry Avisoa Numerical Analysis 60G40, 60H35, 65C20, 65M12, 65K15, 49N70, 49L25, 52B55, 68T07 We propose an implementable, 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. |
| title | Numerical approximation of Dynkin games with asymmetric information |
| topic | Numerical Analysis 60G40, 60H35, 65C20, 65M12, 65K15, 49N70, 49L25, 52B55, 68T07 |
| url | https://arxiv.org/abs/2312.01847 |