eprintid: 10194549 rev_number: 15 eprint_status: archive userid: 699 dir: disk0/10/19/45/49 datestamp: 2024-07-16 13:11:35 lastmod: 2024-08-22 17:59:03 status_changed: 2024-08-22 17:53:10 type: article metadata_visibility: show sword_depositor: 699 creators_name: Pérez, José Luis creators_name: Rodosthenous, Neofytos creators_name: Kazutoshi, Yamazaki title: Nonzero-Sum Optimal Stopping Game with Continuous vs. Periodic Exercise Opportunities ispublished: inpress divisions: UCL divisions: B04 divisions: C06 divisions: F59 note: This version is the author accepted manuscript. For information on re-use, please refer to the publisher's terms and conditions. abstract: We introduce a new nonzero-sum game of optimal stopping with asymmetric exercise opportunities. Given a stochastic process modeling the value of an asset, one player observes and can act on the process continuously, whereas 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, whereas the other one gets nothing. We study how each player balances the maximization of gains against the maximization 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 behavior of the players’ strategies as well as the quantification of the value of available exercise opportunities. date: 2024-07-29 date_type: published publisher: INFORMS official_url: https://doi.org/10.1287/moor.2023.0123 oa_status: green full_text_type: other language: eng primo: open primo_central: open_green verified: verified_manual elements_id: 2296836 doi: 10.1287/moor.2023.0123 lyricists_name: Rodosthenous, Neofytos lyricists_id: NRODO76 actors_name: Rodosthenous, Neofytos actors_id: NRODO76 actors_role: owner full_text_status: public publication: Mathematics of Operations Research citation: Pérez, José Luis; Rodosthenous, Neofytos; Kazutoshi, Yamazaki; (2024) Nonzero-Sum Optimal Stopping Game with Continuous vs. Periodic Exercise Opportunities. Mathematics of Operations Research 10.1287/moor.2023.0123 <https://doi.org/10.1287/moor.2023.0123>. (In press). Green open access document_url: https://discovery.ucl.ac.uk/id/eprint/10194549/1/Perez-Rodosthenous-Yamazaki.pdf