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Optimal stopping games in models with various information flows

Gapeev, Pavel V. and Rodosthenous, Neofytos (2021) Optimal stopping games in models with various information flows. Stochastic Analysis and Applications, 39 (6). 1050 - 1094. ISSN 0736-2994

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Identification Number: 10.1080/07362994.2020.1871013


We study zero-sum optimal stopping games associated with perpetual convertible bonds in an extension of the Black-Merton-Scholes model with random dividends under various information flows. In this type of contracts, the writers have the right to withdraw the bonds, before the holders convert them into assets. We derive closed-form expressions for the associated value function and optimal exercise boundaries in the model with an accessible dividend rate policy which is described by a continuous-time Markov chain with two states. We further consider the optimal stopping game in the model with inaccessible dividend rate policy and prove that the optimal exercise times are the first times at which the asset price process hits monotone boundaries depending on the running state of the filtering dividend rate estimate. We finally present the value of the optimal stopping game for the model in which the dividend rate policy is accessible to the writers but remains inaccessible to the holders of the bonds.

Item Type: Article
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Additional Information: © 2021 Taylor & Francis Group, LLC
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Date Deposited: 04 Jan 2021 15:24
Last Modified: 26 Jan 2022 00:00

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