Browsing by Subject "Random walk"

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    Discrete-time pricing and optimal exercise of American perpetual warrants in the geometric random walk model
    (2013) Vanderbei, R. J.; Pınar, M. Ç.; Bozkaya, E. B.
    An American option (or, warrant) is the right, but not the obligation, to purchase or sell an underlying equity at any time up to a predetermined expiration date for a predetermined amount. A perpetual American option differs from a plain American option in that it does not expire. In this study, we solve the optimal stopping problem of a perpetual American option (both call and put) in discrete time using linear programming duality. Under the assumption that the underlying stock price follows a discrete time and discrete state Markov process, namely a geometric random walk, we formulate the pricing problem as an infinite dimensional linear programming (LP) problem using the excessive-majorant property of the value function. This formulation allows us to solve complementary slackness conditions in closed-form, revealing an optimal stopping strategy which highlights the set of stock-prices where the option should be exercised. The analysis for the call option reveals that such a critical value exists only in some cases, depending on a combination of state-transition probabilities and the economic discount factor (i.e., the prevailing interest rate) whereas it ceases to be an issue for the put.
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    Recognizing faces in news photographs on the web
    (IEEE, 2009-09) Zitouni, Hilal; Bulut, Muhammed Fatih; Duygulu, Pınar
    We propose a graph based method in order to recognize the faces that appear on the web using a small training set. First, relevant pictures of the desired people are collected by querying the name in a text based search engine in order to construct the data set. Then, detected faces in these photographs are represented using SIFT features extracted from facial features. The similarities of faces are represented in a graph which is then used in random walk with restart algorithm to provide links between faces. Those links are used for recognition by using two different methods. © 2009 IEEE.