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Title
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Discounted optimal stopping problems for maxima of geometric brownian motionswith switching payoffs
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Author
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Abstract
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| 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. |
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Language
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English
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Source (journal)
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Advances in applied probability. - Sheffield, 1969, currens
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Publication
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Sheffield
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2021
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ISSN
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0001-8678
[print]
1475-6064
[online]
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DOI
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10.1017/APR.2020.57
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Volume/pages
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53
:1
(2021)
, p. 189-219
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ISI
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000629920200008
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Full text (Publisher's DOI)
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Full text (open access)
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Full text (publisher's version - intranet only)
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