Discounted optimal stopping problems in first-passage time models with random thresholds

Gapeev, Pavel V. ORCID: 0000-0002-1346-2074 and Al Motairi, Hessah (2022) Discounted optimal stopping problems in first-passage time models with random thresholds. Journal of Applied Probability, 59 (3). 714 - 733. ISSN 0021-9002

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Abstract

We derive closed-form solutions to some discounted optimal stopping problems related to the perpetual American cancellable dividend paying put and call option pricing problems in an extension of the Black-Merton-Scholes model. The cancellation times are assumed to occur when the underlying risky asset price process hits some unobservable random thresholds. The optimal stopping times are shown to be the first times at which the asset price reaches stochastic boundaries depending on the current values of its running maximum and minimum processes. 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 and modified normal-reflection conditions. We show that the optimal stopping boundaries are characterised as the maximal and minimal solutions of certain first-order nonlinear ordinary differential equations.

Item Type:	Article
Official URL:	https://www.cambridge.org/core/journals/journal-of...
Additional Information:	© 2022 The Authors
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	20 Apr 2021 12:57
Last Modified:	23 Nov 2024 04:12
URI:	http://eprints.lse.ac.uk/id/eprint/109912

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