Optimal stopping, Appell polynomials, and Wiener–Hopf factorization

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.

Keywords:

• optimal stopping
• Lévy process
• Wiener–Hopf factorization
• Appell polynomial

AMS Subject Classification::

• 60G40
• 60J25
• 60J30
• 60J60
• 60J75