Optimal Stopping Problems and American Options
Date
2006-04-24
Authors
Uys, Nadia
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Abstract
The superharmonic characterization of the value function is proved, under the assumption that an optimal stopping time exists. The fair price of an American
contingent claim is established as an optimal stopping problem. The price of the
perpetual Russian option is derived, using the dual martingale measure to reduce the
dimension of the problem. American barrier options are discussed, and the solution
to the perpetual American up-and-out put is derived. The price of the American put on a finite time horizon is shown to be the price of the European put plus an early exercise premium, through the use of a local time-space formula. The optimal
stopping boundary is characterised as the unique increasing solution of a non-linear
integral equation. Finally, the integral representation of the price of an American
floating strike Asian call with arithmetic averaging is derived.
Description
Degree: Master of Science
Department: Science
Keywords
optimal, stopping problems, american