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Optimal stopping problems for running minima with positive discounting rates

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

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Identification Number: 10.1016/j.spl.2020.108899

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 Sep 2020 11:03
URI: http://eprints.lse.ac.uk/id/eprint/105849

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