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Optimal stopping problems in diffusion-type models with running maxima and drawdowns

Gapeev, Pavel V. and Rodosthenous, Neofytos (2014) Optimal stopping problems in diffusion-type models with running maxima and drawdowns. Journal of Applied Probability, 51 (3). pp. 799-817. ISSN 0021-9002

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Identification Number: 10.1239/jap/1409932675


We study optimal stopping problems related to the pricing of perpetual American options in an extension of the Black-Merton-Scholes model in which the dividend and volatility rates of the underlying risky asset depend on the running values of its maximum and maximum drawdown. The optimal stopping times of the exercise are shown to be the first times at which the price of the underlying asset exits some regions restricted by certain boundaries depending on the running values of the associated maximum and maximum drawdown processes. We obtain closed-form solutions to the equivalent free-boundary problems for the value functions with smooth fit at the optimal stopping boundaries and normal reflection at the edges of the state space of the resulting three-dimensional Markov process. We derive first-order nonlinear ordinary differential equations for the optimal exercise boundaries of the perpetual American standard options.

Item Type: Article
Official URL:
Additional Information: © 2014 Applied Probability Trust
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Date Deposited: 04 Nov 2014 12:14
Last Modified: 20 Oct 2021 00:49

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