Optimal stopping, Appell polynomials and Wiener-Hopf factorization representations of excessive functions of L\'evy processes

In this paper we study the optimal stopping problem for L\'evy processes studied by Novikov and Shiryayev, Stochastics, 2007 In particular, we are interested in finding the representing measure of the value function. It is seen that that this can be expressed in terms of the Appell polynomials. An important tool in our approach and computations is the Wiener-Hopf factorization.