Optimal stopping problems for running minima with positive discounting rates

Gapeev, Pavel V. ORCID: 0000-0002-1346-2074 (2020) Optimal stopping problems for running minima with positive discounting rates. Statistics and Probability Letters, 167. ISSN 0167-7152

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Abstract

We present analytic solutions to some optimal stopping problems for the running minimum of a geometric Brownian motion with exponential positive discounting rates. The proof is based on the reduction of the original problems to the associated free-boundary problems and the solution of the latter problems by means of the smooth-fit and normal-reflection conditions. We show that the optimal stopping boundaries are determined as the minimal solutions of certain first-order nonlinear ordinary differential equations. The obtained results are related to the valuation of perpetual dual American lookback options with fixed and floating strikes in the Black-Merton-Scholes model from the point of view of short sellers.

Item Type:	Article
Official URL:	https://www.sciencedirect.com/journal/statistics-a...
Additional Information:	© 2020 Elsevier B.V.
Divisions:	Mathematics
Subjects:	H Social Sciences > HA Statistics
Date Deposited:	03 Aug 2020 11:15
Last Modified:	07 Oct 2025 05:30
URI:	http://eprints.lse.ac.uk/id/eprint/105849

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