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Abstract
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This is an exposition of some work of S. Levendorskii concerning the use of Wiener-Hopf factorizations for solving some optimal control problems which occur in finance. The basic problem is to find the value of a generalized perpetual American option when the underlying process is Levy. The solution can be written as an iterated integral. The kernels of the integral operators can be explicitly computed in some situations. Levendorskii carries this out by using the fact that the characteristic function of the Levy process with a random exponential time has a Wiener-Hopf factorization. The factorization yields the corresponding characteristic functions for the maximum and minimum of the process. |
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