Excessive functions, appell polynomials and optimal stopping

G5 Doctoral dissertation (article)

Internal Authors/Editors

Publication Details

List of Authors: Bao Quoc Ta
Publisher: Åbo Akademi University
Place: Åbo
Publication year: 2014
ISBN: 978-952-12-3045-5


The main topic of the thesis is optimal stopping. This is treated
in two research articles. In the first article we introduce a new approach
to optimal stopping of general strong Markov processes. The
approach is based on the representation of excessive functions as expected
suprema. We present a variety of examples, in particular, the
Novikov-Shiryaev problem for Lévy processes. In the second article
on optimal stopping we focus on differentiability of excessive functions
of diffusions and apply these results to study the validity of the
principle of smooth fit. As an example we discuss optimal stopping of
sticky Brownian motion. The third research article offers a survey like
discussion on Appell polynomials. The crucial role of Appell polynomials
in optimal stopping of Lévy processes was noticed by Novikov
and Shiryaev. They described the optimal rule in a large class of problems
via these polynomials. We exploit the probabilistic approach to
Appell polynomials and show that many classical results are obtained
with ease in this framework. In the fourth article we derive a new
relationship between the generalized Bernoulli polynomials and the
generalized Euler polynomials.

Last updated on 2020-07-07 at 05:23