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Open AccessArticle

Perpetual American Cancellable Standard Options in Models with Last Passage Times

1
Department of Mathematics, London School of Economics, Houghton Street, London WC2A 2AE, UK
2
School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia
*
Author to whom correspondence should be addressed.
Received: 26 November 2020 / Revised: 18 December 2020 / Accepted: 19 December 2020 / Published: 24 December 2020
(This article belongs to the Special Issue Algorithms for Sequential Analysis)
We derive explicit solutions to the perpetual American cancellable standard put and call options in an extension of the Black–Merton–Scholes model. It is assumed that the contracts are cancelled at the last hitting times for the underlying asset price process of some constant upper or lower levels which are not stopping times with respect to the observable filtration. We show that the optimal exercise times are the first times at which the asset price reaches some lower or upper constant levels. The proof is based on the reduction of the original optimal stopping problems to the associated free-boundary problems and the solution of the latter problems by means of the smooth-fit conditions. View Full-Text
Keywords: perpetual American options; optimal stopping problem; Brownian motion; first passage time; last hitting time; free-boundary problem; instantaneous stopping and smooth fit; a change-of-variable formula with local time on surfaces perpetual American options; optimal stopping problem; Brownian motion; first passage time; last hitting time; free-boundary problem; instantaneous stopping and smooth fit; a change-of-variable formula with local time on surfaces
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MDPI and ACS Style

Gapeev, P.V.; Li, L.; Wu, Z. Perpetual American Cancellable Standard Options in Models with Last Passage Times. Algorithms 2021, 14, 3. https://0-doi-org.brum.beds.ac.uk/10.3390/a14010003

AMA Style

Gapeev PV, Li L, Wu Z. Perpetual American Cancellable Standard Options in Models with Last Passage Times. Algorithms. 2021; 14(1):3. https://0-doi-org.brum.beds.ac.uk/10.3390/a14010003

Chicago/Turabian Style

Gapeev, Pavel V.; Li, Libo; Wu, Zhuoshu. 2021. "Perpetual American Cancellable Standard Options in Models with Last Passage Times" Algorithms 14, no. 1: 3. https://0-doi-org.brum.beds.ac.uk/10.3390/a14010003

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