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
Text (Discounted optimal stopping problems for maxima of geometric Brownian motions with switching payoffs)
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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 |
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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: | 11 Oct 2024 20:18 |
URI: | http://eprints.lse.ac.uk/id/eprint/105811 |
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