Optimal stopping, Appell polynomials, and Wiener–Hopf factorization

Paavo Salminen

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Stochastic processes and financial applications Probability and Statistical Research Probability and Risk Models

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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References

2002Handbook of Brownian Motion - Facts and Formulae 2002Optimal stopping and perpetual options for Lévy processes 1972Optimal Stopping for Partial Sums 2007Optimal stopping of Hunt and Lévy processes 2007On a solution of the optimal stopping problem for processes with independent increments 2005On the Novikov-Shiryaev Optimal Stopping Problems in Continuous Time 2007An approach for solving perpetual optimal stopping problems driven by Lévy processes

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