NDLI: Optimal Stopping Problems in Diffusion-Type Models with Running Maxima and Drawdowns

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Optimal Stopping Problems in Diffusion-Type Models with Running Maxima and Drawdowns

Content Provider	Scilit
Author	Gapeev, Pavel V. Rodosthenous, Neofytos
Copyright Year	2014
Description	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. c2 Postal address: University of Leeds, School of Mathematics, Leeds LS2 9JT, UK. Email address: n.rodosthenous@leeds.ac.uk
Related Links	http://arxiv.org/pdf/1405.4438 http://journals.cambridge.org/article_S000186780001168X
Ending Page	817
Page Count	19
Starting Page	799
ISSN	00219002
e-ISSN	14756072
DOI	10.1017/s000186780001168x
Journal	Journal of applied probability
Issue Number	3
Volume Number	51
Language	English
Publisher	Cambridge University Press (CUP)
Publisher Date	2014-09-01
Access Restriction	Open
Subject Keyword	Journal of applied probability Operations Research and Management Science Multidimensional Optimal Stopping Problem Brownian Motion Running Maximum and Running Maximum Drawdown Process boundary Problem Instantaneous Stopping and Smooth Fit Normal Reflection variable Formula with Local Time On Surfaces Perpetual American Option
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Statistics, Probability and Uncertainty

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