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

Gapeev, Pavel V., 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:	17 Apr 2024 01:15
URI:	http://eprints.lse.ac.uk/id/eprint/105811

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