The optimal control of a Lévy process

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Title: The optimal control of a Lévy process
Author: DiTanna, Anthony Santino
Abstract: In this thesis we study the optimal stochastic control problem of the drift of a Lévy process . We show that , for a broad class of Lévy processes , the partial integro -differential Hamilton -Jacobi -Bellman equation for the value function admits classical solutions and that control policies exist in feedback form . We then explore the class of Lévy processes that satisfy the requirements of the theorem , and find connections between the uniform integrability requirement and the notions of the score function and Fisher information from information theory . Finally we present three different numerical implementations of the control problem : a traditional dynamic programming approach , and two iterative approaches , one based on a finite difference scheme and the other on the Fourier transform .
URI: http : / /hdl .handle .net /2152 /6652
Date: 2009-10-23


The optimal control of a Lévy process. Doctoral dissertation, The University of Texas at Austin. Available electronically from http : / /hdl .handle .net /2152 /6652 .

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