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Stochastics
An International Journal of Probability and Stochastic Processes
Volume 83, 2011 - Issue 4-6: Optimal stopping with Applications
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Original Articles

Optimal stopping, Appell polynomials, and Wiener–Hopf factorization

Pages 611-622 | Received 04 Dec 2009, Accepted 04 Jan 2011, Published online: 10 Mar 2011
 

Abstract

In this paper, we study the Novikov–Shiryaev optimal stopping problem for Lévy processes. In particular, we are interested in finding the representing measure of the value function. It is seen that this can be expressed in terms of the Appell polynomials. For spectrally one-sided Lévy processes, the results are appealing and explicit. An important tool in our approach and computations is the Wiener–Hopf factorization.

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