Discounted optimal stopping problems for maxima of geometric Brownian motions with switching payoffs

Gapeev, Pavel V. ORCID: 0000-0002-1346-2074, Kort, Peter M. and Lavrutich, Maria (2021) Discounted optimal stopping problems for maxima of geometric Brownian motions with switching payoffs. Advances in Applied Probability, 53 (1). 189 - 219. ISSN 0001-8678

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Abstract

We present closed-form solutions to some discounted optimal stopping problems for the running maximum of a geometric Brownian motion with payoffs switching according to the dynamics of a continuous-time Markov chain with two states. The proof is based on the reduction of the original problems to the equivalent 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 maximal solutions of the associated two-dimensional systems of first-order nonlinear ordinary differential equations. The obtained results are related to the valuation of real switching lookback options with fixed and floating sunk costs in the Black–Merton–Scholes model.

Item Type:	Article
Official URL:	https://www.cambridge.org/core/journals/advances-i...
Additional Information:	© 2021 The Authors
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	29 Jul 2020 09:03
Last Modified:	12 Dec 2024 02:15
URI:	http://eprints.lse.ac.uk/id/eprint/105811

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