Non-zero-sum optimal stopping game with continuous versus periodic exercise opportunities
Fuente:
arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866917665818279936 |
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| author | Pérez, José Luis Rodosthenous, Neofytos Yamazaki, Kazutoshi |
| author_facet | Pérez, José Luis Rodosthenous, Neofytos Yamazaki, Kazutoshi |
| contents | We introduce a new non-zero-sum game of optimal stopping with asymmetric exercise opportunities. Given a stochastic process modelling the value of an asset, one player observes and can act on the process continuously, while the other player can act on it only periodically at independent Poisson arrival times. The first one to stop receives a reward, different for each player, while the other one gets nothing. We study how each player balances the maximisation of gains against the maximisation of the likelihood of stopping before the opponent. In such a setup, driven by a Lévy process with positive jumps, we not only prove the existence, but also explicitly construct a Nash equilibrium with values of the game written in terms of the scale function. Numerical illustrations with put-option payoffs are also provided to study the behaviour of the players' strategies as well as the quantification of the value of available exercise opportunities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2107_08243 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Non-zero-sum optimal stopping game with continuous versus periodic exercise opportunities Pérez, José Luis Rodosthenous, Neofytos Yamazaki, Kazutoshi Probability 60G51, 60G40, 91A15, 90B50 We introduce a new non-zero-sum game of optimal stopping with asymmetric exercise opportunities. Given a stochastic process modelling the value of an asset, one player observes and can act on the process continuously, while the other player can act on it only periodically at independent Poisson arrival times. The first one to stop receives a reward, different for each player, while the other one gets nothing. We study how each player balances the maximisation of gains against the maximisation of the likelihood of stopping before the opponent. In such a setup, driven by a Lévy process with positive jumps, we not only prove the existence, but also explicitly construct a Nash equilibrium with values of the game written in terms of the scale function. Numerical illustrations with put-option payoffs are also provided to study the behaviour of the players' strategies as well as the quantification of the value of available exercise opportunities. |
| title | Non-zero-sum optimal stopping game with continuous versus periodic exercise opportunities |
| topic | Probability 60G51, 60G40, 91A15, 90B50 |
| url | https://arxiv.org/abs/2107.08243 |