Browsing by Subject "Difference equations."
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Item Open Access Feature extraction with the fractional Fourier transform(Bilkent University, 1998) Güleryüz, ÖzgürIn this work, alternative design and implementation techniques for feature extraction applications are proposed. The proposed techniques amount to decomposing the overall feature extraction problem into a global linear system followed by a local nonlinear system. Different output representations for representation of input features are also allowed and used in these techniques. These different output representations bring cui additional degree of freedom to the feature extraction problems. The systems provide multi-outputs consisting of different features of the input signal or image. Efficient implementation of the linear part of the .system is obtained by using fractional Fourier filtering circuits. Expressions for the proposed techniques are derived and several illustrative examples cxre given in which efficient implementations for feature extraction applications are obtained.Item Open Access Pricing and optimal exercise of perpetual American options with linear programming(Bilkent University, 2010) Bozkaya, Efe BurakAn American option 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 with methods from the linear programming literature. Under the assumption that the underlying’s price follows a discrete time and discrete state Markov process, we formulate the problem with an infinite dimensional linear program using the excessive and majorant properties of the value function. This formulation allows us to solve complementary slackness conditions efficiently, revealing an optimal stopping strategy which highlights the set of stock-prices for which the option should be exercised. Under two different stock-price movement scenarios (simple and geometric random walks), we show that the optimal strategy is to exercise the option when the stock-price hits a special critical value. The analysis also reveals that such a critical value exists only for some special cases under the geometric random walk, dependent on a combination of state-transition probabilities and the economic discount factor. We further demonstrate that the method is useful for determining the optimal stopping time for combinations of plain vanilla options, by solving the same problem for spread and strangle positions under simple random walks.